Question

How do you simplify the radical expression `sqrt72`?

Answer 1

`sqrt72 = sqrt(36xx26)=sqrt36xxsqrt2 = 6xxsqrt2`

Explanation:

This takes advantage of the relation

`sqrt(axxb)=sqrtaxxsqrtb`

Look for a factor in the original value that is a perfect square (4, 9, 16, 25, 36, etc.)

Answer 2

`6sqrt(2)`

Explanation:

(I think you meant as a simplified radical, so that's what I'm going to answer.)
`sqrt(72)` can also be thought of as `sqrt(36*2)`, or `sqrt(6*6*2)`.
Using the rule that `sqrt(ab)=sqrt(a)*sqrt(b)`, you end up with `sqrt(6)*sqrt(6)*sqrt(2)`.
This can also be expressed as `sqrt(6)^2*sqrt(2)`.
The square root and square cancel, leaving us with the simplified radical of `6sqrt(2)`.