Most people simplify radicals by looking for perfect square factors, but this is an alternative method that works for other roots besides square roots. Create a factor tree, and look at only the bottom, prime number leaves. If you're doing a square root, pairs of numbers represent a factor outside the radical; a cube root, trios of the same number, and so forth. Any prime "leaf" that is left without a pair (or trio) will remain inside the radical.
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