Simplify Square Root of 81582

What is the square root of 81582 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.

√81582 = A√B

Unfortunately, the square root of 81582 cannot be simplified. Thus, here is the answer to the square root of 81582 in its simplest form:

√ 81582 = √ 81582

Here are two different methods we used to determine why the square root of 81582 cannot be simplified.

1) To be able to simplify the square root of 81582, one of the factors of 81582 other than 1 must be a perfect square. The factors of 81582 are 1, 2, 3, 6, 13597, 27194, 40791, and 81582. Since none of these factors are perfect squares, the square root of 81582 cannot be simplified.

2) To be able to simplify the square root of 81582, all the prime factors of 81582 cannot be unique. When we did prime factorization of 81582, we found that 2 x 3 x 13597 equals 81582. Since all the prime factors are unique, the square root of 81582 cannot be simplified.

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