Lesson 2, Topic 2
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# Square Root of Numbers

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Given the square of these numbers find the square root:

a. 4Â  x 4Â  =Â  16, The square root of 16 isÂ  written asÂ  $$\scriptsize \sqrt{16}= 4$$
b. 5 x 5Â  =Â  25, The square root of 25,Â $$\scriptsize \sqrt{25}= 5$$
c. 3 x 3Â  = 9, The square root of 9 , Â Â $$\scriptsize \sqrt{9}= 3$$

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 -5Â  =Â  25, Â  The square root of 25,Â $$\scriptsize \sqrt{25}= 5$$

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

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

$$\scriptsize \sqrt{25} \\ \scriptsize = \sqrt{5 \: \times \: 5}\\ \scriptsize = \sqrt{-5 \: \times \: -5}\\ \scriptsize = \pm{5}$$

### Example

Find the square root ofÂ

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

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