Simplify Square Root of 84413

What is the square root of 84413 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.

√84413 = A√B

Unfortunately, the square root of 84413 cannot be simplified. Thus, here is the answer to the square root of 84413 in its simplest form:

√ 84413 = √ 84413

Here are two different methods we used to determine why the square root of 84413 cannot be simplified.

1) To be able to simplify the square root of 84413, one of the factors of 84413 other than 1 must be a perfect square. The factors of 84413 are 1, 7, 31, 217, 389, 2723, 12059, and 84413. Since none of these factors are perfect squares, the square root of 84413 cannot be simplified.

2) To be able to simplify the square root of 84413, all the prime factors of 84413 cannot be unique. When we did prime factorization of 84413, we found that 7 x 31 x 389 equals 84413. Since all the prime factors are unique, the square root of 84413 cannot be simplified.

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