Simplify Square Root of 82819

What is the square root of 82819 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.

√82819 = A√B

Unfortunately, the square root of 82819 cannot be simplified. Thus, here is the answer to the square root of 82819 in its simplest form:

√ 82819 = √ 82819

Here are two different methods we used to determine why the square root of 82819 cannot be simplified.

1) To be able to simplify the square root of 82819, one of the factors of 82819 other than 1 must be a perfect square. The factors of 82819 are 1, 11, 7529, and 82819. Since none of these factors are perfect squares, the square root of 82819 cannot be simplified.

2) To be able to simplify the square root of 82819, all the prime factors of 82819 cannot be unique. When we did prime factorization of 82819, we found that 11 x 7529 equals 82819. Since all the prime factors are unique, the square root of 82819 cannot be simplified.

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