Simplify Square Root of 86581

What is the square root of 86581 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.

√86581 = A√B

Unfortunately, the square root of 86581 cannot be simplified. Thus, here is the answer to the square root of 86581 in its simplest form:

√ 86581 = √ 86581

Here are two different methods we used to determine why the square root of 86581 cannot be simplified.

1) To be able to simplify the square root of 86581, one of the factors of 86581 other than 1 must be a perfect square. The factors of 86581 are 1, 11, 17, 187, 463, 5093, 7871, and 86581. Since none of these factors are perfect squares, the square root of 86581 cannot be simplified.

2) To be able to simplify the square root of 86581, all the prime factors of 86581 cannot be unique. When we did prime factorization of 86581, we found that 11 x 17 x 463 equals 86581. Since all the prime factors are unique, the square root of 86581 cannot be simplified.

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