Simplify Square Root of 32171

What is the square root of 32171 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√32171 = A√B

Unfortunately, the square root of 32171 cannot be simplified. Thus, here is the answer to the square root of 32171 in its simplest form:

√ 32171 = √ 32171

Here are two different methods we used to determine why the square root of 32171 cannot be simplified.

1) To be able to simplify the square root of 32171, one of the factors of 32171 other than 1 must be a perfect square. The factors of 32171 are 1, 53, 607, and 32171. Since none of these factors are perfect squares, the square root of 32171 cannot be simplified.

2) To be able to simplify the square root of 32171, all the prime factors of 32171 cannot be unique. When we did prime factorization of 32171, we found that 53 x 607 equals 32171. Since all the prime factors are unique, the square root of 32171 cannot be simplified.

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