Simplify Square Root of 81782

What is the square root of 81782 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.

√81782 = A√B

Unfortunately, the square root of 81782 cannot be simplified. Thus, here is the answer to the square root of 81782 in its simplest form:

√ 81782 = √ 81782

Here are two different methods we used to determine why the square root of 81782 cannot be simplified.

1) To be able to simplify the square root of 81782, one of the factors of 81782 other than 1 must be a perfect square. The factors of 81782 are 1, 2, 103, 206, 397, 794, 40891, and 81782. Since none of these factors are perfect squares, the square root of 81782 cannot be simplified.

2) To be able to simplify the square root of 81782, all the prime factors of 81782 cannot be unique. When we did prime factorization of 81782, we found that 2 x 103 x 397 equals 81782. Since all the prime factors are unique, the square root of 81782 cannot be simplified.

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