Question

Question #46f3e

Answer 1

Let us assume a square root....

Explanation:

Assuming that we are simplifying a square root (rather than a cube root, fourth root, or other radical), we are looking for perfect squares that divide 108. It helps to factor 108 completely into primes.

`108 = 2*54`

`108 = 2*2*27`

`108 = 2*2*3*9`

FINALLY, we have:

`108 = 2*2*3*3*3`

Since we are searching for perfect squares, any pair of identical factors IS a perfect square. Perfect squares extract as a single factor of their type.

`2*2` extracts as a `2`.

`3*3` extracts as a `3`.

The remaining `3` stays under the radical.

So

`sqrt(108) = 2*3*sqrt(3)`.

Multiply the factors that are outside.

`sqrt(108) = 6sqrt(3)`