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.

Exampe 1

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 2

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

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