Simplify Square Root of 83021

What is the square root of 83021 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.

√83021 = A√B

Unfortunately, the square root of 83021 cannot be simplified. Thus, here is the answer to the square root of 83021 in its simplest form:

√ 83021 = √ 83021

Here are two different methods we used to determine why the square root of 83021 cannot be simplified.

1) To be able to simplify the square root of 83021, one of the factors of 83021 other than 1 must be a perfect square. The factors of 83021 are 1, 61, 1361, and 83021. Since none of these factors are perfect squares, the square root of 83021 cannot be simplified.

2) To be able to simplify the square root of 83021, all the prime factors of 83021 cannot be unique. When we did prime factorization of 83021, we found that 61 x 1361 equals 83021. Since all the prime factors are unique, the square root of 83021 cannot be simplified.

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