Simplify Square Root of 84971

What is the square root of 84971 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.

√84971 = A√B

Unfortunately, the square root of 84971 cannot be simplified. Thus, here is the answer to the square root of 84971 in its simplest form:

√ 84971 = √ 84971

Here are two different methods we used to determine why the square root of 84971 cannot be simplified.

1) To be able to simplify the square root of 84971, one of the factors of 84971 other than 1 must be a perfect square. The factors of 84971 are 1, 31, 2741, and 84971. Since none of these factors are perfect squares, the square root of 84971 cannot be simplified.

2) To be able to simplify the square root of 84971, all the prime factors of 84971 cannot be unique. When we did prime factorization of 84971, we found that 31 x 2741 equals 84971. Since all the prime factors are unique, the square root of 84971 cannot be simplified.

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