Simplify Square Root of 52186

What is the square root of 52186 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.

√52186 = A√B

Unfortunately, the square root of 52186 cannot be simplified. Thus, here is the answer to the square root of 52186 in its simplest form:

√ 52186 = √ 52186

Here are two different methods we used to determine why the square root of 52186 cannot be simplified.

1) To be able to simplify the square root of 52186, one of the factors of 52186 other than 1 must be a perfect square. The factors of 52186 are 1, 2, 97, 194, 269, 538, 26093, and 52186. Since none of these factors are perfect squares, the square root of 52186 cannot be simplified.

2) To be able to simplify the square root of 52186, all the prime factors of 52186 cannot be unique. When we did prime factorization of 52186, we found that 2 x 97 x 269 equals 52186. Since all the prime factors are unique, the square root of 52186 cannot be simplified.

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