Simplify Square Root of 82729

What is the square root of 82729 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.

√82729 = A√B

Unfortunately, the square root of 82729 cannot be simplified. Thus, here is the answer to the square root of 82729 in its simplest form:

√ 82729 = √ 82729

Here are two different methods we used to determine why the square root of 82729 cannot be simplified.

1) To be able to simplify the square root of 82729, one of the factors of 82729 other than 1 must be a perfect square. The factors of 82729 are 1 and 82729. Since none of these factors are perfect squares, the square root of 82729 cannot be simplified.

2) To be able to simplify the square root of 82729, all the prime factors of 82729 cannot be unique. When we did prime factorization of 82729, we found that 82729 equals 82729. Since all the prime factors are unique, the square root of 82729 cannot be simplified.

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