Simplify Square Root of 56689

What is the square root of 56689 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.

√56689 = A√B

Unfortunately, the square root of 56689 cannot be simplified. Thus, here is the answer to the square root of 56689 in its simplest form:

√ 56689 = √ 56689

Here are two different methods we used to determine why the square root of 56689 cannot be simplified.

1) To be able to simplify the square root of 56689, one of the factors of 56689 other than 1 must be a perfect square. The factors of 56689 are 1, 83, 683, and 56689. Since none of these factors are perfect squares, the square root of 56689 cannot be simplified.

2) To be able to simplify the square root of 56689, all the prime factors of 56689 cannot be unique. When we did prime factorization of 56689, we found that 83 x 683 equals 56689. Since all the prime factors are unique, the square root of 56689 cannot be simplified.

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