Simplify Square Root of 80686

What is the square root of 80686 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.

√80686 = A√B

Unfortunately, the square root of 80686 cannot be simplified. Thus, here is the answer to the square root of 80686 in its simplest form:

√ 80686 = √ 80686

Here are two different methods we used to determine why the square root of 80686 cannot be simplified.

1) To be able to simplify the square root of 80686, one of the factors of 80686 other than 1 must be a perfect square. The factors of 80686 are 1, 2, 40343, and 80686. Since none of these factors are perfect squares, the square root of 80686 cannot be simplified.

2) To be able to simplify the square root of 80686, all the prime factors of 80686 cannot be unique. When we did prime factorization of 80686, we found that 2 x 40343 equals 80686. Since all the prime factors are unique, the square root of 80686 cannot be simplified.

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