Simplify Square Root of 56566

What is the square root of 56566 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.

√56566 = A√B

Unfortunately, the square root of 56566 cannot be simplified. Thus, here is the answer to the square root of 56566 in its simplest form:

√ 56566 = √ 56566

Here are two different methods we used to determine why the square root of 56566 cannot be simplified.

1) To be able to simplify the square root of 56566, one of the factors of 56566 other than 1 must be a perfect square. The factors of 56566 are 1, 2, 28283, and 56566. Since none of these factors are perfect squares, the square root of 56566 cannot be simplified.

2) To be able to simplify the square root of 56566, all the prime factors of 56566 cannot be unique. When we did prime factorization of 56566, we found that 2 x 28283 equals 56566. Since all the prime factors are unique, the square root of 56566 cannot be simplified.

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