Simplify Square Root of 83359

What is the square root of 83359 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.

√83359 = A√B

Unfortunately, the square root of 83359 cannot be simplified. Thus, here is the answer to the square root of 83359 in its simplest form:

√ 83359 = √ 83359

Here are two different methods we used to determine why the square root of 83359 cannot be simplified.

1) To be able to simplify the square root of 83359, one of the factors of 83359 other than 1 must be a perfect square. The factors of 83359 are 1, 31, 2689, and 83359. Since none of these factors are perfect squares, the square root of 83359 cannot be simplified.

2) To be able to simplify the square root of 83359, all the prime factors of 83359 cannot be unique. When we did prime factorization of 83359, we found that 31 x 2689 equals 83359. Since all the prime factors are unique, the square root of 83359 cannot be simplified.

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