Simplify Square Root of 58397

What is the square root of 58397 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.

√58397 = A√B

Unfortunately, the square root of 58397 cannot be simplified. Thus, here is the answer to the square root of 58397 in its simplest form:

√ 58397 = √ 58397

Here are two different methods we used to determine why the square root of 58397 cannot be simplified.

1) To be able to simplify the square root of 58397, one of the factors of 58397 other than 1 must be a perfect square. The factors of 58397 are 1, 23, 2539, and 58397. Since none of these factors are perfect squares, the square root of 58397 cannot be simplified.

2) To be able to simplify the square root of 58397, all the prime factors of 58397 cannot be unique. When we did prime factorization of 58397, we found that 23 x 2539 equals 58397. Since all the prime factors are unique, the square root of 58397 cannot be simplified.

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