Simplify Square Root of 82513

What is the square root of 82513 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.

√82513 = A√B

Unfortunately, the square root of 82513 cannot be simplified. Thus, here is the answer to the square root of 82513 in its simplest form:

√ 82513 = √ 82513

Here are two different methods we used to determine why the square root of 82513 cannot be simplified.

1) To be able to simplify the square root of 82513, one of the factors of 82513 other than 1 must be a perfect square. The factors of 82513 are 1, 109, 757, and 82513. Since none of these factors are perfect squares, the square root of 82513 cannot be simplified.

2) To be able to simplify the square root of 82513, all the prime factors of 82513 cannot be unique. When we did prime factorization of 82513, we found that 109 x 757 equals 82513. Since all the prime factors are unique, the square root of 82513 cannot be simplified.

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