Simplify Square Root of 83321

What is the square root of 83321 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.

√83321 = A√B

Unfortunately, the square root of 83321 cannot be simplified. Thus, here is the answer to the square root of 83321 in its simplest form:

√ 83321 = √ 83321

Here are two different methods we used to determine why the square root of 83321 cannot be simplified.

1) To be able to simplify the square root of 83321, one of the factors of 83321 other than 1 must be a perfect square. The factors of 83321 are 1, 7, 11903, and 83321. Since none of these factors are perfect squares, the square root of 83321 cannot be simplified.

2) To be able to simplify the square root of 83321, all the prime factors of 83321 cannot be unique. When we did prime factorization of 83321, we found that 7 x 11903 equals 83321. Since all the prime factors are unique, the square root of 83321 cannot be simplified.

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