Simplify Square Root of 39718

What is the square root of 39718 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.

√39718 = A√B

Unfortunately, the square root of 39718 cannot be simplified. Thus, here is the answer to the square root of 39718 in its simplest form:

√ 39718 = √ 39718

Here are two different methods we used to determine why the square root of 39718 cannot be simplified.

1) To be able to simplify the square root of 39718, one of the factors of 39718 other than 1 must be a perfect square. The factors of 39718 are 1, 2, 7, 14, 2837, 5674, 19859, and 39718. Since none of these factors are perfect squares, the square root of 39718 cannot be simplified.

2) To be able to simplify the square root of 39718, all the prime factors of 39718 cannot be unique. When we did prime factorization of 39718, we found that 2 x 7 x 2837 equals 39718. Since all the prime factors are unique, the square root of 39718 cannot be simplified.

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