Simplify Square Root of 41686

What is the square root of 41686 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.

√41686 = A√B

Unfortunately, the square root of 41686 cannot be simplified. Thus, here is the answer to the square root of 41686 in its simplest form:

√ 41686 = √ 41686

Here are two different methods we used to determine why the square root of 41686 cannot be simplified.

1) To be able to simplify the square root of 41686, one of the factors of 41686 other than 1 must be a perfect square. The factors of 41686 are 1, 2, 19, 38, 1097, 2194, 20843, and 41686. Since none of these factors are perfect squares, the square root of 41686 cannot be simplified.

2) To be able to simplify the square root of 41686, all the prime factors of 41686 cannot be unique. When we did prime factorization of 41686, we found that 2 x 19 x 1097 equals 41686. Since all the prime factors are unique, the square root of 41686 cannot be simplified.

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