Question

How to simplify square root of 72?

Answer 1

Answer: $\sqrt[6]{2}$

Step-by-step explanation: The easiest way to do this problem is to factor 72 as 2 · 36 then recognise 36 as a perfect square, 6 · 6.

There is no need to factor further because the 6's pair up. So a 6 comes out of the radical leaving a 2 inside and our answer is $\sqrt[6]{2}$.

As you make your factor tree, always be on the lookout for perfect squares such as 36.

I have shown my work in the image attached.

Answer 2

6√2

√72
= √8*9
= √(4*2*9)
= √4*√2*√9
= 2*3*√2
= 6√2