Question

How do you simplify `sqrt(72)`?

Answer 1

`sqrt72 = 6sqrt2`

Explanation:

Check to see if `72` is divisible by a perfect square:
`2^2 = 4` and `72 = 4*18`
So `sqrt72 = sqrt(4*18) = sqrt4*sqrt18 =2sqrt18`

Continue be checking to see is `18` is divisible by a perfect square:
`2^2 = 4`, and `18` is not divisible by `4`
`3^2=9` and `18=9*2`

so we get:
`sqrt72 = 2sqrt18 = 2sqrt(9*2)=2sqrt9sqrt2=2*3sqrt3=6sqrt2`

There are many ways of writing/working this simplification. Here are a few more:

`sqrt72 = sqrt(4*9*2) = 2*3*sqrt2 = 6sqrt2`

`sqrt72 = sqrt (36*2) = sqrt36sqrt2=6sqrt2`

`sqrt72 = sqrt(2^3*3^2) = sqrt(2^2*2*3^2) = 2*sqrt2*3 = 6sqrt2`