Simplify Square Root of 85261

What is the square root of 85261 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.

√85261 = A√B

Unfortunately, the square root of 85261 cannot be simplified. Thus, here is the answer to the square root of 85261 in its simplest form:

√ 85261 = √ 85261

Here are two different methods we used to determine why the square root of 85261 cannot be simplified.

1) To be able to simplify the square root of 85261, one of the factors of 85261 other than 1 must be a perfect square. The factors of 85261 are 1, 11, 23, 253, 337, 3707, 7751, and 85261. Since none of these factors are perfect squares, the square root of 85261 cannot be simplified.

2) To be able to simplify the square root of 85261, all the prime factors of 85261 cannot be unique. When we did prime factorization of 85261, we found that 11 x 23 x 337 equals 85261. Since all the prime factors are unique, the square root of 85261 cannot be simplified.

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