Lesson 2, Topic 4
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# Addition and Subtraction of Square Roots

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To add or subtract numbers inside a square root sign, deal with the arithmetic operation first before finding the square root of the answer.

For example:

Calculate $$\scriptsize \sqrt{3 + 6}$$

Add the two numbers $$\scriptsize \sqrt{3 + 6} = \sqrt{9}$$

Then find the square root.

Calculate $$\scriptsize \sqrt{9} = 3$$

This is the correct way of solving it

$$\scriptsize \sqrt{3 + 6} = \sqrt{9} = 3$$

### Example

Calculate
a. $$\scriptsize \sqrt{24 + 12}$$
b. $$\scriptsize \sqrt{26 + 74}$$
c. $$\scriptsize \sqrt{102 \;-\; 38}$$
d. $$\scriptsize \sqrt{24 + 50 \;- \;38}$$

Solution

a. $$\scriptsize \sqrt{24 \:+ \: 12} \\ \scriptsize = \sqrt{36}\\ \scriptsize = 3$$

b. $$\scriptsize \sqrt{26 \:+ \: 74} \\ \scriptsize = \sqrt{100}\\ \scriptsize = 10$$

c. $$\scriptsize \sqrt{102\:- \:38} \\ \scriptsize = \sqrt{64} \\ \scriptsize = 8$$

d. $$\scriptsize \sqrt{24 \:+ \:50 \:- \:38} \\ \scriptsize = \sqrt{74\:- \:38} \\ \scriptsize= \sqrt{36} \\ \scriptsize = 6$$

Evaluation Questions:

A. Use factors to find the square root of the following:

1.  16
2.  400
3.  625
4.  441
5.  1600
6.  2500
7.  784
8.  7744
9.  3136
10.  3600

B. Find the smallest number by which the following must be multiplied so that their products are perfect squares.

1. 84
2. 90
3. 24
4. 54
5. 50
6. 40
7. 100
8. 252
9. 360
10. 140

error: