Simplify Square Root of 84817

What is the square root of 84817 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.

√84817 = A√B

Unfortunately, the square root of 84817 cannot be simplified. Thus, here is the answer to the square root of 84817 in its simplest form:

√ 84817 = √ 84817

Here are two different methods we used to determine why the square root of 84817 cannot be simplified.

1) To be able to simplify the square root of 84817, one of the factors of 84817 other than 1 must be a perfect square. The factors of 84817 are 1, 89, 953, and 84817. Since none of these factors are perfect squares, the square root of 84817 cannot be simplified.

2) To be able to simplify the square root of 84817, all the prime factors of 84817 cannot be unique. When we did prime factorization of 84817, we found that 89 x 953 equals 84817. Since all the prime factors are unique, the square root of 84817 cannot be simplified.

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