Let us assume a square root....
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.
FINALLY, we have:
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.
Multiply the factors that are outside.