Simplify Square Root of 85039

What is the square root of 85039 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.

√85039 = A√B

Unfortunately, the square root of 85039 cannot be simplified. Thus, here is the answer to the square root of 85039 in its simplest form:

√ 85039 = √ 85039

Here are two different methods we used to determine why the square root of 85039 cannot be simplified.

1) To be able to simplify the square root of 85039, one of the factors of 85039 other than 1 must be a perfect square. The factors of 85039 are 1, 277, 307, and 85039. Since none of these factors are perfect squares, the square root of 85039 cannot be simplified.

2) To be able to simplify the square root of 85039, all the prime factors of 85039 cannot be unique. When we did prime factorization of 85039, we found that 277 x 307 equals 85039. Since all the prime factors are unique, the square root of 85039 cannot be simplified.

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