Addition and Subtraction of Square Roots

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

\(\scriptsize \sqrt{3 + 6} = \sqrt{9} = 3\)

Worked Example 2.4.1:

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

Remember “BODMAS”. To solve question “d” we add first before subtracting.

Evaluation Questions: