Square Numbers & Square Roots of NumbersChris James
The document discusses squaring numbers and finding square roots. It explains that to square a number, you multiply a number by itself. Some examples given are that 12 equals 1, 22 equals 4, and 32 equals 9. It also explains that the square root of a number is the opposite of squaring - so the square root of 4 is 2 because 22 equals 4. More examples of square roots are given such as the square root of 9 being 3 because 32 equals 9. The document encourages visiting an external website for more math help and games.
A pattern is a sequence of numbers, shapes, or other objects that follows a specific rule such as repeating, growing, or both. Number patterns can be repeating, growing, or a combination of both. Examples of number patterns include skip counting, repeating numbers, and growing numbers. Geometric patterns also follow specific rules with repeating shapes or letters. The document provides examples of number patterns and problems involving number patterns to solve.
This document provides methods for calculating the square of various types of numbers:
1) For numbers ending in 5, add 1 to the digit before 5 and multiply it by that digit. Then write 25 after it (e.g. 225 for 15x15).
2) For numbers with all the same digit, write the digits in ascending then descending order (e.g. 12321 for 111x111).
3) For two-digit numbers starting with 5, take the square of the first digit and second digit separately and concatenate them (e.g. 2704 for 52x52).
4) For two-digit numbers starting with 9, subtract from 100, take the square of
The document discusses square roots and radicals. It defines the square root operation as extracting the number that, when squared, equals the number inside the radical. It provides a table of common square numbers and their square roots that should be memorized. It also describes how to estimate the square root of numbers between known square numbers using the table as a reference.
Power Series,Taylor's and Maclaurin's SeriesShubham Sharma
A details explanation about Taylor's and Maclaurin's series with variety of examples are included in this slide. The aim is to give the viewer the basic knowledge about the topic.
The document discusses square numbers and square roots. It defines a square number as a number that can be represented as a perfect square array, with each small square having a side length of 1. A square root is the number that, when multiplied by itself, equals the original number. The document provides examples of perfect squares and their square roots, and methods for finding the square root of larger numbers by factoring them into smaller perfect squares.
The document contains examples of solving various types of algebraic equations including:
1) Equations with multiplication and subtraction or addition such as 2x - 4 = 8 and 5x + 10 = 80.
2) Equations with fractions such as 2/3x + 2 = 8.
3) Equations involving division such as x/5 + 2 = 8.
4) Equations with collecting like terms such as 4x + 6x + 20 = 80.
5) Equations using the distributive property such as 10x – 3x -12 = 4x – 9x + 48.
This document provides an introduction to adding integers using number chips. It explains that integers can be positive or negative whole numbers. Examples are provided of representing positive and negative integers as number chips that can cancel each other out when added. Step-by-step workings are shown for adding combinations of positive and negative integers using this model of number chips. Practice problems are provided for the student to try.
Square Numbers & Square Roots of NumbersChris James
The document discusses squaring numbers and finding square roots. It explains that to square a number, you multiply a number by itself. Some examples given are that 12 equals 1, 22 equals 4, and 32 equals 9. It also explains that the square root of a number is the opposite of squaring - so the square root of 4 is 2 because 22 equals 4. More examples of square roots are given such as the square root of 9 being 3 because 32 equals 9. The document encourages visiting an external website for more math help and games.
A pattern is a sequence of numbers, shapes, or other objects that follows a specific rule such as repeating, growing, or both. Number patterns can be repeating, growing, or a combination of both. Examples of number patterns include skip counting, repeating numbers, and growing numbers. Geometric patterns also follow specific rules with repeating shapes or letters. The document provides examples of number patterns and problems involving number patterns to solve.
This document provides methods for calculating the square of various types of numbers:
1) For numbers ending in 5, add 1 to the digit before 5 and multiply it by that digit. Then write 25 after it (e.g. 225 for 15x15).
2) For numbers with all the same digit, write the digits in ascending then descending order (e.g. 12321 for 111x111).
3) For two-digit numbers starting with 5, take the square of the first digit and second digit separately and concatenate them (e.g. 2704 for 52x52).
4) For two-digit numbers starting with 9, subtract from 100, take the square of
The document discusses square roots and radicals. It defines the square root operation as extracting the number that, when squared, equals the number inside the radical. It provides a table of common square numbers and their square roots that should be memorized. It also describes how to estimate the square root of numbers between known square numbers using the table as a reference.
Power Series,Taylor's and Maclaurin's SeriesShubham Sharma
A details explanation about Taylor's and Maclaurin's series with variety of examples are included in this slide. The aim is to give the viewer the basic knowledge about the topic.
The document discusses square numbers and square roots. It defines a square number as a number that can be represented as a perfect square array, with each small square having a side length of 1. A square root is the number that, when multiplied by itself, equals the original number. The document provides examples of perfect squares and their square roots, and methods for finding the square root of larger numbers by factoring them into smaller perfect squares.
The document contains examples of solving various types of algebraic equations including:
1) Equations with multiplication and subtraction or addition such as 2x - 4 = 8 and 5x + 10 = 80.
2) Equations with fractions such as 2/3x + 2 = 8.
3) Equations involving division such as x/5 + 2 = 8.
4) Equations with collecting like terms such as 4x + 6x + 20 = 80.
5) Equations using the distributive property such as 10x – 3x -12 = 4x – 9x + 48.
This document provides an introduction to adding integers using number chips. It explains that integers can be positive or negative whole numbers. Examples are provided of representing positive and negative integers as number chips that can cancel each other out when added. Step-by-step workings are shown for adding combinations of positive and negative integers using this model of number chips. Practice problems are provided for the student to try.
Properties of Square Numbers (Class 8) (Audio in Hindi)Parth Nagpal
This presentation was created by me for the Scholars for Change Campaign, IIM Ahmedabad for the underprivileged children.
Scholars for Change is a campaign of Education Innovation Bank at IIM Ahmedabad. This campaign seeks to give to underprivileged children access to high quality, interesting content in Science and Math, so that they can learn on their own, in their own language, with fun and play.
The document describes a method for extracting square roots mentally without a calculator. It involves memorizing the squares of the first 10 numbers, and using properties of squared numbers to determine the tens and ones digits of the square root. For a given number, the tens place is identified by finding the largest square less than or equal to the number's left digits. Then properties of 5's squares help determine the ones place digit. Several examples demonstrate how to apply this method to find square roots of 4-digit numbers mentally.
Here are the steps to find the x and y intercepts of the given equations:
1. 3x + 5y = 30
X-intercept: Put 0 in for y. 3x + 5(0) = 30. 3x = 30. x = 10
Y-intercept: Put 0 in for x. 3(0) + 5y = 30. 5y = 30. y = 6
2. 4x + 2y = 12
X-intercept: Put 0 in for y. 4x + 2(0) = 12. 4x = 12. x = 3
Y-intercept: Put 0 in for x. 4(0) + 2y = 12. 2y
The document defines domain and range. Domain is the set of all possible input values of a function. Range is the set of all output values of a function as the input variable takes on all possible values. It then verifies the domain and range of several functions, including square root, square, and inverse functions. It also evaluates compositions of functions where f(x)=x^2 and g(x)=x-3. Finally, it evaluates compositions of functions where f(x)=sqrt(x), g(x)=x/2, and h(x)=x-8.
The document discusses squares and square roots, explaining that a square number is the product of a whole number multiplied by itself, and can be represented by arranging objects in a square pattern. It provides examples of calculating square roots by factoring numbers into smaller perfect squares. The document also describes how to estimate square roots for non-perfect squares by interpolating between the adjacent perfect square numbers.
The document provides examples and explanations for adding integers on a number line and in expressions. It includes warm-up problems, examples of writing integer addition modeled on number lines, evaluating integer expressions, and an application problem about plane altitude relative to sea level using integer addition. The document is a lesson on adding integers with examples to practice the skill.
This document provides notes and practice questions for a GCSE maths exam. It covers several topics that may appear on the non-calculator paper, including: factorizing expressions; BIDMAS order of operations; algebraic notation; angles; scatter graphs; stem and leaf plots; linear equations; and sequences. It also includes full worked examples and explanations of key concepts.
The document provides information about topics covered in math class today including:
- Reviewing for the final exam by practicing adding, subtracting, multiplying, and dividing fractions.
- Using the Pythagorean theorem and distance formula to solve problems finding the distance between two points on a graph or with coordinates.
- Examples are given for using the distance formula when all four coordinates are known or when three are known and the distance is solved for.
- A review of graphing terminology like quadrants, the origin, and ordering of x and y coordinates.
The document discusses three ways to manipulate array data: searching, accumulating, and reversing elements. It provides code examples to search an array for a value and return its index, add corresponding elements of two arrays into a third array, and read numbers into an array and print them in reverse order.
This document provides 15 examples of word problems involving numbers. Each example presents a multi-step word problem, shows the steps to define variables, write equations, and solve for the unknown values. The examples cover a range of problem types including finding missing numbers based on relationships between amounts, averages, sums, differences, products, and ratios.
1. The document contains 19 math problems from various topics including calculus, algebra, geometry, probability, and number theory. The problems range in complexity from computing simple expressions to word problems involving multiple steps.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
The document provides rules for adding or removing brackets when performing mathematical operations involving addition, subtraction, multiplication, and division. It explains that for addition and subtraction, the signs inside brackets do not change when brackets are added or removed. However, for multiplication and division, the signs inside brackets change when brackets are added or removed - multiplication signs change to division signs and vice versa. Several examples are given to illustrate each of these rules.
Weekly Dose 10 - Maths Olympiad PracticeKathleen Ong
The document presents a word problem involving percentages of students participating in various sports. It then shows the step-by-step solution to determine the minimum percentage of students who participated in all four sports based on the percentages given for each individual sport. The minimum percentage is found by assuming each student misses at most one sport and calculating the percentage of students who participated in all four as 100% minus the sum of the percentages who did not participate in each sport.
The document provides important facts and formulae related to numbers. It discusses the following key points:
1. The Hindu-Arabic numeral system uses 10 digits (0-9) to represent any number. A group of digits forming a number is called a numeral.
2. Types of numbers include natural numbers, whole numbers, integers, even/odd numbers, prime/composite numbers. Tests for divisibility by various numbers are outlined.
3. Shortcut methods for multiplication like distributive law are described. Basic formulae for exponents, progressions, and the division algorithm are listed.
The document contains solutions to 7 probability questions involving dice rolls, card draws, balls drawn from urns/bags. The solutions calculate the total possible outcomes and favorable outcomes to determine the probability of various events. For example, the probability of rolling a double on two dice is 1/6, drawing a black card from a deck is 1/2, and drawing a white ball from a bag with 3 red, 5 black and 4 white balls is 4/12.
This document contains solutions to 9 questions about plotting graphs from tabular data. The solutions involve representing the variables in the tables on the x and y axes and plotting the points to form line graphs. Bar charts are also created from some of the data. The data relates to topics like hospital patient numbers over time, crop yields for farmers, relationships between variables like time/workers and task completion, and cricket scoring across overs.
Properties of Square Numbers (Class 8) (Audio in Hindi)Parth Nagpal
This presentation was created by me for the Scholars for Change Campaign, IIM Ahmedabad for the underprivileged children.
Scholars for Change is a campaign of Education Innovation Bank at IIM Ahmedabad. This campaign seeks to give to underprivileged children access to high quality, interesting content in Science and Math, so that they can learn on their own, in their own language, with fun and play.
The document describes a method for extracting square roots mentally without a calculator. It involves memorizing the squares of the first 10 numbers, and using properties of squared numbers to determine the tens and ones digits of the square root. For a given number, the tens place is identified by finding the largest square less than or equal to the number's left digits. Then properties of 5's squares help determine the ones place digit. Several examples demonstrate how to apply this method to find square roots of 4-digit numbers mentally.
Here are the steps to find the x and y intercepts of the given equations:
1. 3x + 5y = 30
X-intercept: Put 0 in for y. 3x + 5(0) = 30. 3x = 30. x = 10
Y-intercept: Put 0 in for x. 3(0) + 5y = 30. 5y = 30. y = 6
2. 4x + 2y = 12
X-intercept: Put 0 in for y. 4x + 2(0) = 12. 4x = 12. x = 3
Y-intercept: Put 0 in for x. 4(0) + 2y = 12. 2y
The document defines domain and range. Domain is the set of all possible input values of a function. Range is the set of all output values of a function as the input variable takes on all possible values. It then verifies the domain and range of several functions, including square root, square, and inverse functions. It also evaluates compositions of functions where f(x)=x^2 and g(x)=x-3. Finally, it evaluates compositions of functions where f(x)=sqrt(x), g(x)=x/2, and h(x)=x-8.
The document discusses squares and square roots, explaining that a square number is the product of a whole number multiplied by itself, and can be represented by arranging objects in a square pattern. It provides examples of calculating square roots by factoring numbers into smaller perfect squares. The document also describes how to estimate square roots for non-perfect squares by interpolating between the adjacent perfect square numbers.
The document provides examples and explanations for adding integers on a number line and in expressions. It includes warm-up problems, examples of writing integer addition modeled on number lines, evaluating integer expressions, and an application problem about plane altitude relative to sea level using integer addition. The document is a lesson on adding integers with examples to practice the skill.
This document provides notes and practice questions for a GCSE maths exam. It covers several topics that may appear on the non-calculator paper, including: factorizing expressions; BIDMAS order of operations; algebraic notation; angles; scatter graphs; stem and leaf plots; linear equations; and sequences. It also includes full worked examples and explanations of key concepts.
The document provides information about topics covered in math class today including:
- Reviewing for the final exam by practicing adding, subtracting, multiplying, and dividing fractions.
- Using the Pythagorean theorem and distance formula to solve problems finding the distance between two points on a graph or with coordinates.
- Examples are given for using the distance formula when all four coordinates are known or when three are known and the distance is solved for.
- A review of graphing terminology like quadrants, the origin, and ordering of x and y coordinates.
The document discusses three ways to manipulate array data: searching, accumulating, and reversing elements. It provides code examples to search an array for a value and return its index, add corresponding elements of two arrays into a third array, and read numbers into an array and print them in reverse order.
This document provides 15 examples of word problems involving numbers. Each example presents a multi-step word problem, shows the steps to define variables, write equations, and solve for the unknown values. The examples cover a range of problem types including finding missing numbers based on relationships between amounts, averages, sums, differences, products, and ratios.
1. The document contains 19 math problems from various topics including calculus, algebra, geometry, probability, and number theory. The problems range in complexity from computing simple expressions to word problems involving multiple steps.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
The document provides rules for adding or removing brackets when performing mathematical operations involving addition, subtraction, multiplication, and division. It explains that for addition and subtraction, the signs inside brackets do not change when brackets are added or removed. However, for multiplication and division, the signs inside brackets change when brackets are added or removed - multiplication signs change to division signs and vice versa. Several examples are given to illustrate each of these rules.
Weekly Dose 10 - Maths Olympiad PracticeKathleen Ong
The document presents a word problem involving percentages of students participating in various sports. It then shows the step-by-step solution to determine the minimum percentage of students who participated in all four sports based on the percentages given for each individual sport. The minimum percentage is found by assuming each student misses at most one sport and calculating the percentage of students who participated in all four as 100% minus the sum of the percentages who did not participate in each sport.
The document provides important facts and formulae related to numbers. It discusses the following key points:
1. The Hindu-Arabic numeral system uses 10 digits (0-9) to represent any number. A group of digits forming a number is called a numeral.
2. Types of numbers include natural numbers, whole numbers, integers, even/odd numbers, prime/composite numbers. Tests for divisibility by various numbers are outlined.
3. Shortcut methods for multiplication like distributive law are described. Basic formulae for exponents, progressions, and the division algorithm are listed.
The document contains solutions to 7 probability questions involving dice rolls, card draws, balls drawn from urns/bags. The solutions calculate the total possible outcomes and favorable outcomes to determine the probability of various events. For example, the probability of rolling a double on two dice is 1/6, drawing a black card from a deck is 1/2, and drawing a white ball from a bag with 3 red, 5 black and 4 white balls is 4/12.
This document contains solutions to 9 questions about plotting graphs from tabular data. The solutions involve representing the variables in the tables on the x and y axes and plotting the points to form line graphs. Bar charts are also created from some of the data. The data relates to topics like hospital patient numbers over time, crop yields for farmers, relationships between variables like time/workers and task completion, and cricket scoring across overs.
The document defines various terms related to quadrilaterals and regular polygons. It then provides solutions to 19 questions involving calculating missing angle measures, identifying properties, and determining the number of sides of regular polygons given the measure of each interior angle. The questions cover properties of quadrilaterals like total angle sum, relationships between adjacent/opposite angles and sides, using angle measures to find unknown angles, and properties of regular polygons.
This document contains solutions to 7 questions about classifying and drawing different types of curves and polygons. It defines open and closed curves, and classifies example curves. It also defines properties of polygons like regular polygons, convex/concave polygons, and calculates the number of diagonals in different polygons. Examples include drawing a polygon with its interior shaded and diagonals, classifying curves as simple/closed/polygons, and naming regular polygons with different numbers of sides.
The document discusses properties of polyhedrons and Euler's formula. It begins by defining a tetrahedron as having the minimum number of planes (4) to enclose a solid. It then answers questions about possible face configurations of polyhedrons and applies Euler's formula, which relates the number of faces, vertices and edges. Specifically, it states that a polyhedron can have any number of faces if it has 4 or more. It also equates a square prism to a cube. Finally, it works through examples verifying and applying Euler's formula to calculate unknown values for various polyhedrons.
This document contains 35 multi-part math word problems involving the volume, surface area, radius, height, diameter, and other properties of cylinders. The problems provide these cylinder dimensions and ask the reader to calculate various volume, area, ratio, and other metrics. Sample solutions are provided that show the calculations for determining these values based on the cylinder geometry formulas of volume, surface area, etc.
The document contains 14 multiple choice and short answer questions about properties of rhombi and parallelograms. Key points covered include:
- A rhombus is a parallelogram with 4 equal sides and diagonals that bisect each other at right angles.
- Properties of rhombi include having two pairs of parallel sides, two pairs of equal sides, and diagonals that bisect angles.
- A square is a special type of rhombus where all 4 angles are right angles.
- Questions involve identifying properties, constructing figures based on given properties, and calculating unknown values using properties of rhombi and parallelograms.
This document contains 17 multi-part questions about calculating the surface areas and volumes of cubes, cuboids, and other shapes. The solutions show the formulas used and step-by-step workings to find the requested dimensions, areas, volumes, or costs. For example, Question 1 calculates the surface areas of cuboids with given lengths, breadths, and heights. Question 17 calculates the breadth of a school hall given its length, height, door/window areas, and total whitewashing cost.
This document contains 10 questions about key statistical concepts like observations, raw data, frequency distributions, class intervals, and constructing frequency tables from data sets. For each question, it provides the definitions or explanations of terms and shows the step-by-step work of arranging data, determining values like range and frequency, and creating frequency distribution tables to organize and summarize the data.
This document contains 27 math word problems with solutions. The problems involve calculating percentages, rates of change, ratios, and other calculations. Some key details extracted from across the problems include:
- Calculating percentages of totals like 22% of 120, 25% of Rs. 1000, etc.
- Finding original values given final values and percentage increases/decreases like if a 10% increase results in Rs. 3575, what was the original salary?
- Sharing totals according to given percentages, like sharing Rs. 3500 according to 50% ratios.
- Calculating population changes over time given annual percentage increases.
- Determining component percentages in alloys or mixtures.
8. Question 2.
Find the least number which must be subtracted from the following numbers
to make them a perfect square :
9. (i) 2361
(ii) 194491
(iii) 26535
(iv) 16160
(v) 4401624
Solution:
(i) 2361
Finding the square root of 2361
We get 48 as quotient and remainder = 57
∴ To make it a perfect square, we have to subtract 57 from 2361
∴ Least number to be subtracted = 57
(ii) 194491
Finding the square root of 194491
We get 441 as quotient and remainder = 10
∴ To make it a perfect square, we have to subtract 10 from 194491
∴ Least number to be subtracted = 10
(iii) 26535
Finding the square root of 26535
We get 162 as quotient and 291 as remainder
∴ To make it a perfect square, we have to subtract 291 from 26535
∴ Least number to be subtracted = 291
(iv)16160
Finding the square root of 16160
10. We get 127 as quotient and 31 as remainder
∴ To make it a perfect square, we have to subtract 31 from 16160
∴ Least number to be subtracted = 31
(v) 4401624
Find the square root of 4401624
We get 2098 as quotient and 20 as remainder
∴ To make it a perfect square, we have to subtract 20 from 4401624
∴ Least number to be subtracted = 20
Question 3.
Find the least number which must be added to the following numbers to make them
a perfect square :
(i) 5607
(ii) 4931
(iii) 4515600
(iv) 37460
(v) 506900
Solution:
(i) 5607
Finding the square root of 5607, we see that 742
= 5607- 131 =5476 and 752
= 5625
∴ 5476 < 5607 < 5625
∴ 5625 – 5607 = 18 is to be added to get a perfect square
∴ Least number to be added = 18
11. (ii) 4931
Finding the square root of 4931, we see that 702
= 4900
∴ 712
= 5041 4900 <4931 <5041
∴ 5041 – 4931 = 110 is to be added to get a perfect square.
∴ Least number to be added =110
(iii) 4515600
Finding the square root of 4515600, we see
that 21242
= 4511376
and 2 1 252
= 45 1 56 25
∴ 4511376 <4515600 <4515625
∴ 4515625 – 4515600 = 25 is to be added to get a perfect square.
∴ Least number to be added = 25
(iv) 37460
Finding the square root of 37460
that 1932
= 37249, 1942
= =37636
∴ 37249 < 37460 < 37636
∴ 37636 – 37460 = 176 is to be added to get a perfect square.
∴ Least number to be added =176
(v) 506900
12. Finding the square root of 506900, we see that
7112
= 505521, 7122
= 506944
∴ 505521 < 506900 < 506944
∴ 506944 – 506900 = 44 is to be added to get a perfect square.
∴ Least number to be added = 44
Question 4.
Find the greatest number of 5 digits which is a perfect square.
Solution:
Greatest number of 5-digits = 99999 Finding square root, we see that 143 is left as
remainder
∴ Perfect square = 99999 – 143 = 99856 If we add 1 to 99999, it will because a
number of 6 digits
∴ Greatest square 5-digits perfect square = 99856
Question 5.
Find the least number of four digits which is a perfect square.
Solution:
Least number of 4-digits = 10000
Finding square root of 1000
We see that if we subtract 39
From 1000, we get three digit number
∴ We shall add 124 – 100 = 24 to 1000 to get a
13. perfect square of 4-digit number
∴ 1000 + 24 = 1024
∴ Least number of 4-digits which is a perfect square = 1024
Question 6.
Find the least number of six-digits which is a perfect square.
Solution:
Least number of 6-digits = 100000
Finding the square root of 100000, we see that if we subtract 544, we get a perfect
square of 5-digits.
So we shall add
4389 – 3900 = 489
to 100000 to get a perfect square
Past perfect square of six digits= 100000 + 489 =100489
Question 7.
Find the greatest number of 4-digits which is a perfect square.
Solution:
Greatest number of 4-digits = 9999
Finding the square root, we see that 198 has been left as remainder
∴ 4-digit greatest perfect square = 9999 – 198 = 9801
Question 8.
A General arranges his soldiers in rows to form a perfect square. He finds that in
doing so, 60 soldiers are left out. If the total number of soldiers be 8160, find the
number of soldiers in each row.
Solution:
Total number of soldiers = 8160 Soldiers left after arranging them in a square = 60
14. ∴ Number of soldiers which are standing in a square = 8160 – 60 = 8100
Question 9.
The area of a square field is 60025 m2
. A man cycle along its boundry at 18 km/hr. In
how much time will be return at the starting point.
Solution:
Area of a square field = 60025 m2
Question 10.
The cost of levelling and turfing a square lawn at Rs. 250 per m2
is Rs. 13322.50.
Find the cost of fencing it at Rs. 5 per metre ?
Solution:
15. Cost of levelling a square field = Rs. 13322.50
Rate of levelling = Rs. 2.50 per m2
and perimeter = 4a = 4 x 73 = 292 m Rate of fencing the field = Rs. 5 per m
∴ Total cost of fencing = Rs. 5 x 292 = Rs. 1460
Question 11.
Find the greatest number of three digits which is a perfect square.
Solution:
3-digits greatest number = 999
Finding the square root, we see that 38 has been left
∴ Perfect square = 999 – 38 = 961
∴ Greatest 3-digit perfect square = 961
Question 12.
Find the smallest number which must be added to 2300 so that it becomes a perfect
square.
Solution:
Finding the square root of 2300
We see that we have to add 704 – 700 = 4 to 2300 in order to get a perfect square
∴ Smallest number to be added = 4