Simplify Square Root of 85757

What is the square root of 85757 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.

√85757 = A√B

Unfortunately, the square root of 85757 cannot be simplified. Thus, here is the answer to the square root of 85757 in its simplest form:

√ 85757 = √ 85757

Here are two different methods we used to determine why the square root of 85757 cannot be simplified.

1) To be able to simplify the square root of 85757, one of the factors of 85757 other than 1 must be a perfect square. The factors of 85757 are 1, 7, 12251, and 85757. Since none of these factors are perfect squares, the square root of 85757 cannot be simplified.

2) To be able to simplify the square root of 85757, all the prime factors of 85757 cannot be unique. When we did prime factorization of 85757, we found that 7 x 12251 equals 85757. Since all the prime factors are unique, the square root of 85757 cannot be simplified.

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