Lesson 2, Topic 2
In Progress

# Square Root of Numbers

Lesson Progress
0% Complete

Given the square of these numbers find the square root:

a. 4  x 4  =  16, The square root of 16 is  written as  $$\scriptsize \sqrt{16}= 4$$

b. 5 x 5  =  25, The square root of 25, $$\scriptsize \sqrt{25}= 5$$

c. 3 x 3  = 9, The square root of 9 ,   $$\scriptsize \sqrt{9}= 3$$

This implies that the square root of a given number is that number that multiplies itself to give the given number.

Similarly,

d. -4 x -4 = 16, The square root of $$\scriptsize \sqrt{16}= 4$$

e. -5 x -5  =  25,   The square root of 25, $$\scriptsize \sqrt{25}= 5$$

In general, a number has two square roots: one negative square root and one positive square root.

e.g.$$\scriptsize \sqrt{16}= \sqrt{4 \; \times \; 4}= \sqrt{-4 \; \times \; -4}$$

=$$\scriptsize \pm{4}$$

$$\scriptsize \sqrt{25}= \sqrt{5 \; \times \; 5}= \sqrt{-5 \; \times \; -5}$$

=$$\scriptsize \pm{5}$$

Example

Find the square root of

a. 144

b. 81

c. 324

d. 900

Solution

a. Square root  of  144 = $$\scriptsize \sqrt{144}$$

Step 1: Express 144 as product of prime factors.

Step 2:

144   = (2 x 2) x (2x 2) x (3 x 3)

$$\scriptsize \sqrt{144}$$   = 2 x 2 x 3

$$\scriptsize \sqrt{144}$$   = 12

b. Square  root of 81  =   $$\scriptsize \sqrt{81}$$

Step 1:

=  81 = 3 x 3 x 3 x 3

Step 2:

$$\scriptsize \sqrt{81}$$  = 3 x 3 = 9

c. Square root of  324 =  $$\scriptsize \sqrt{324}$$

Step 1:

324 = 2 x 2 x 3 x 3 x 3 x 3

Step 2:

$$\scriptsize \sqrt{324}$$ = 2 x 3 x 3 = 18

d. Square root of 900   =  $$\scriptsize \sqrt{900}$$

Step 1

Step 2:

$$\scriptsize \sqrt{900}$$  = 2 x 3 x 5

= 30 error: