Suppose you need to simplify the square root of a number. The easiest way to do this is to break the number under the radical sign into factos, one of which is a perfect square. For example,

square root(84)

Get factors of 84, one of which is a perect square. We could choose 2 and 42, but neither of those is a perfect square, so it's better to choose 4 and 21.

Therefore,

square root(84) = square root(4) * square root(21)

We know the square root of 4 is 2, therefore

square root(84) = 2square root(21).

Since the only factors of 21 are 1, 3, 7 and 21, all of which are not perfect squares,

square root(21) cannot be simplified.

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