The document provides an introduction to square roots, detailing their mathematical definition and importance. It explains how to find square roots through factorization and includes examples for both whole numbers and fractions, as well as exercises. Additionally, it addresses word problems involving square roots, demonstrating practical applications.

1. Nazish Jamali
BS Education Batch-16

2. Square Root

3. Introduction
• A number that produces a specified
number when it is multiplies by itself.
OR
Square root of a number is a value that,
when multiplied by itself, gives the
number.

4. Examples
i. 4 x 4 = 16,
4 is called the square root of 16.
ii. (−4) × (−4) = 16,
so −4 is also a square root of 16.

5. • This means every number has two square
roots, one is positive another one is
negative, but the square root of number is
always positive.
•
called the radical.
• For example: √36 = 6 , (because 6 x 6 =36

6. • "Squared" is often written as a little 2 like
this:
This says "4 Squared equals 16"

7. Finding Square
Root Of
Numbers

8. square root by Factorization
01. √256
= √2x2x2x2x2x2x2x2
= 2x2x2x2
= 16
Verification: 16 x 16 = 256
2 256
2 128
2 64
2 32
2 16
2 8
2 4
2 2
1

9. Exercise 4.1
12. √2025
= √3x3x3x3x5x5
= 3x3x5
=45
3 2025
3 675
3 225
3 75
5 25
5 5
1

10. Square root of common fractions
The following rule is to be remembered for
obtaining the square root of a common
fraction.
Square root of fraction = square root of numerator / square root of denominator
If p and q be two natural numbers, then the square root of
P²/q²
is expressed as, √ P²/q² = √ P² / √ q² = √pxp / √qxq = p/q

11. Example
Find the square root of 64/81
Sol:
√64/81
= √64/ √81
= √8x8 / √9x9
= 8/9

12. Square root of Decimal friction
We first convert it into a common fraction
and then find the square root by the
method of finding the square root of
common fractions. The result obtained
changed into decimal fraction.

13. Example
1. Find the square root of 1.44
Sol: √1.44 = √144 / 100
= √3x3x2x2x2x2 / 5x5x2x2
= √3²x2²x2² / 5²x2²
= 3x2x2 / 5x2
= 12/10 = 1.2

14. Word Problems on square root
Example:
The area of a square park is 169 sq.m. what is the length of a side of
the park?
Sol:
Length of the area = √Area of the square park
= √169
= √13x13
=13m

15. Thank You