Simplify Square Root of 85058

What is the square root of 85058 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.

√85058 = A√B

Unfortunately, the square root of 85058 cannot be simplified. Thus, here is the answer to the square root of 85058 in its simplest form:

√ 85058 = √ 85058

Here are two different methods we used to determine why the square root of 85058 cannot be simplified.

1) To be able to simplify the square root of 85058, one of the factors of 85058 other than 1 must be a perfect square. The factors of 85058 are 1, 2, 71, 142, 599, 1198, 42529, and 85058. Since none of these factors are perfect squares, the square root of 85058 cannot be simplified.

2) To be able to simplify the square root of 85058, all the prime factors of 85058 cannot be unique. When we did prime factorization of 85058, we found that 2 x 71 x 599 equals 85058. Since all the prime factors are unique, the square root of 85058 cannot be simplified.

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