Simplify Square Root of 39931

What is the square root of 39931 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.

√39931 = A√B

Unfortunately, the square root of 39931 cannot be simplified. Thus, here is the answer to the square root of 39931 in its simplest form:

√ 39931 = √ 39931

Here are two different methods we used to determine why the square root of 39931 cannot be simplified.

1) To be able to simplify the square root of 39931, one of the factors of 39931 other than 1 must be a perfect square. The factors of 39931 are 1, 73, 547, and 39931. Since none of these factors are perfect squares, the square root of 39931 cannot be simplified.

2) To be able to simplify the square root of 39931, all the prime factors of 39931 cannot be unique. When we did prime factorization of 39931, we found that 73 x 547 equals 39931. Since all the prime factors are unique, the square root of 39931 cannot be simplified.

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