Simplify Square Root of 61591

What is the square root of 61591 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.

√61591 = A√B

Unfortunately, the square root of 61591 cannot be simplified. Thus, here is the answer to the square root of 61591 in its simplest form:

√ 61591 = √ 61591

Here are two different methods we used to determine why the square root of 61591 cannot be simplified.

1) To be able to simplify the square root of 61591, one of the factors of 61591 other than 1 must be a perfect square. The factors of 61591 are 1, 17, 3623, and 61591. Since none of these factors are perfect squares, the square root of 61591 cannot be simplified.

2) To be able to simplify the square root of 61591, all the prime factors of 61591 cannot be unique. When we did prime factorization of 61591, we found that 17 x 3623 equals 61591. Since all the prime factors are unique, the square root of 61591 cannot be simplified.

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