Simplify Square Root of 31993

What is the square root of 31993 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.

√31993 = A√B

Unfortunately, the square root of 31993 cannot be simplified. Thus, here is the answer to the square root of 31993 in its simplest form:

√ 31993 = √ 31993

Here are two different methods we used to determine why the square root of 31993 cannot be simplified.

1) To be able to simplify the square root of 31993, one of the factors of 31993 other than 1 must be a perfect square. The factors of 31993 are 1, 13, 23, 107, 299, 1391, 2461, and 31993. Since none of these factors are perfect squares, the square root of 31993 cannot be simplified.

2) To be able to simplify the square root of 31993, all the prime factors of 31993 cannot be unique. When we did prime factorization of 31993, we found that 13 x 23 x 107 equals 31993. Since all the prime factors are unique, the square root of 31993 cannot be simplified.

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