Irrational number
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The document discusses square roots and how to estimate them to varying degrees of precision. It defines the principal root as the positive square root of a number. It provides examples of perfect squares and their roots. It explains that irrational numbers are those that cannot be expressed as a ratio of integers, like π. The document then gives steps to estimate square roots to the nearest tenths or hundredths place by considering the closest perfect squares before and after the given number.
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If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
https://tinyurl.com/y9muob6q
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The document discusses different types of real numbers including rational and irrational numbers. It provides examples and definitions of natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It also includes information on Euclid's division algorithm and its application in finding highest common factors and lowest common multiples. Examples of proving the irrationality of square roots like √5 are given.
Maths project
The document discusses different types of real numbers including rational and irrational numbers. It provides examples and definitions of natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It also includes information on Euclid's division algorithm and its application in finding the highest common factor of two numbers. Examples are provided to illustrate the algorithm.
ROOTS AND RADICALS - ELEMENTARY ALGEBRA
1. The document provides an overview of roots and radicals, including definitions of square roots, principal and negative square roots, radical expressions, rational and irrational numbers, and methods for simplifying, adding, subtracting, multiplying, dividing, and rationalizing radicals.
2. Square roots are factors whose product is the radicand, and the principal square root is the positive root. Radicals indicate roots and have a radicand and index. Rational numbers can be expressed as ratios while irrational numbers cannot.
3. Graphs and tables can be used to find approximate square roots. Radicals can be simplified using properties of exponents and fractions. Radical equations are solved by isolating the radical and taking squares of both
1. basic concepts (1)
This document provides definitions and examples related to divisibility tests, LCM, HCF, and properties of square numbers, square roots, cubes, cube roots, and indices. It gives the definitions of LCM as the least number divisible by all numbers in a set and HCF as the highest number that divides all numbers in a set. It provides properties and examples for determining if a number is divisible by numbers 2 through 11. It also provides characteristics and examples for determining properties of square numbers, their square roots, cubes, and cube roots based on their endings. The document concludes with examples of working with indices, including simplifying expressions and solving problems using indices concepts.
1 chap
This document provides information on numbers and numerical concepts in 3 sentences:
It defines key terms like numeral, place value, and face value. It also categorizes different types of numbers such as natural numbers, whole numbers, integers, even/odd numbers, and prime/composite numbers. Finally, it outlines tests for divisibility and formulas for operations like multiplication, progression, and division.
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Irrational number
- 1. Subtitle
- 2. Principal Root The positive square root of a number is called the principal root. 12 = (1 x 1) = 1 22 = (2 x 2) = 4 32 = (3 . 3) = 9 42 = (4) (4) = 16 52 = (5) (5) = 25 (-1)2 = 1 (-2)2 = 4 (-3)2 = 9 (-4)2 = 16 (-5)2 = 25
- 3. Irrational numbers (H) ▪ The set of irrational numbers is the set of numbers which cannot be expressed as a ratio of two integers. These numbers are equivalent to non-terminating and non-repeating decimals. Examples: 2 ; π = 3.1416… ; 5 ; 8 ; 17
- 4. To determine the integers before and after the square root of a number, think of a perfect square number before and after the given number. Then, solve for the roots. Example 1: 11 9 = 3 (since 3 . 3 is 9) and 16 = 4 (since 4 . 4 is 16) Therefore, 11 is between 3 and 4. Example 2: 156 144 = 12 and 169 = 13 Therefore, 156 is between 12 and 13.
- 5. Example 3: 74 64 = 8 and 81 = 9 Therefore, 74 is between 8 and 9. Example 4: 35 25 = 5 and 36 = 6 Therefore, 35 is between 5 and 6.
- 6. To estimate the square root of a number to the nearest tenths and hundredths: ▪ 1. Think of two closest perfect square numbers before and after the given number. ▪ 2. Solve for the roots and the use the first as the whole number. ▪ 3. Solve for the tenths digit by dividing the difference of the first perfect square number from the given number by the difference of the first perfect square number from the second perfect square number. ▪ 4 To estimate the square root of a number to the nearest hundredths, identify a number whose square is closest to the given number.
- 7. Example 1. What is 𝟕 ? 4 = 2 and 9 = 3 so, it is between 2 and 3. Let 7 = 2. x 7 −4 9 −4 = 3 5 = 0.6 Therefore the estimated square root of 7 to the nearest tenths is 2. 6
- 8. To find the estimated hundredths, 2.64 < 7 < 2. 65 (2.64)2 = 6.9696 and (2.65)2 = 7.0225 Therefore the estimated square root of 7 to the nearest hundredths is 2.65