Simplify Square Root of 31697

What is the square root of 31697 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.

√31697 = A√B

Unfortunately, the square root of 31697 cannot be simplified. Thus, here is the answer to the square root of 31697 in its simplest form:

√ 31697 = √ 31697

Here are two different methods we used to determine why the square root of 31697 cannot be simplified.

1) To be able to simplify the square root of 31697, one of the factors of 31697 other than 1 must be a perfect square. The factors of 31697 are 1, 29, 1093, and 31697. Since none of these factors are perfect squares, the square root of 31697 cannot be simplified.

2) To be able to simplify the square root of 31697, all the prime factors of 31697 cannot be unique. When we did prime factorization of 31697, we found that 29 x 1093 equals 31697. Since all the prime factors are unique, the square root of 31697 cannot be simplified.

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