Simplify Square Root of 36631

What is the square root of 36631 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.

√36631 = A√B

Unfortunately, the square root of 36631 cannot be simplified. Thus, here is the answer to the square root of 36631 in its simplest form:

√ 36631 = √ 36631

Here are two different methods we used to determine why the square root of 36631 cannot be simplified.

1) To be able to simplify the square root of 36631, one of the factors of 36631 other than 1 must be a perfect square. The factors of 36631 are 1, 7, 5233, and 36631. Since none of these factors are perfect squares, the square root of 36631 cannot be simplified.

2) To be able to simplify the square root of 36631, all the prime factors of 36631 cannot be unique. When we did prime factorization of 36631, we found that 7 x 5233 equals 36631. Since all the prime factors are unique, the square root of 36631 cannot be simplified.

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