Simplify Square Root of 5707

What is the square root of 5707 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.

√5707 = A√B

Unfortunately, the square root of 5707 cannot be simplified. Thus, here is the answer to the square root of 5707 in its simplest form:

√ 5707 = √ 5707

Here are two different methods we used to determine why the square root of 5707 cannot be simplified.

1) To be able to simplify the square root of 5707, one of the factors of 5707 other than 1 must be a perfect square. The factors of 5707 are 1, 13, 439, and 5707. Since none of these factors are perfect squares, the square root of 5707 cannot be simplified.

2) To be able to simplify the square root of 5707, all the prime factors of 5707 cannot be unique. When we did prime factorization of 5707, we found that 13 x 439 equals 5707. Since all the prime factors are unique, the square root of 5707 cannot be simplified.

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