Simplify Square Root of 82658

What is the square root of 82658 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.

√82658 = A√B

Unfortunately, the square root of 82658 cannot be simplified. Thus, here is the answer to the square root of 82658 in its simplest form:

√ 82658 = √ 82658

Here are two different methods we used to determine why the square root of 82658 cannot be simplified.

1) To be able to simplify the square root of 82658, one of the factors of 82658 other than 1 must be a perfect square. The factors of 82658 are 1, 2, 37, 74, 1117, 2234, 41329, and 82658. Since none of these factors are perfect squares, the square root of 82658 cannot be simplified.

2) To be able to simplify the square root of 82658, all the prime factors of 82658 cannot be unique. When we did prime factorization of 82658, we found that 2 x 37 x 1117 equals 82658. Since all the prime factors are unique, the square root of 82658 cannot be simplified.

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