Simplify Square Root of 81739

What is the square root of 81739 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.

√81739 = A√B

Unfortunately, the square root of 81739 cannot be simplified. Thus, here is the answer to the square root of 81739 in its simplest form:

√ 81739 = √ 81739

Here are two different methods we used to determine why the square root of 81739 cannot be simplified.

1) To be able to simplify the square root of 81739, one of the factors of 81739 other than 1 must be a perfect square. The factors of 81739 are 1, 7, 11677, and 81739. Since none of these factors are perfect squares, the square root of 81739 cannot be simplified.

2) To be able to simplify the square root of 81739, all the prime factors of 81739 cannot be unique. When we did prime factorization of 81739, we found that 7 x 11677 equals 81739. Since all the prime factors are unique, the square root of 81739 cannot be simplified.

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