Simplify Square Root of 39674

What is the square root of 39674 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.

√39674 = A√B

Unfortunately, the square root of 39674 cannot be simplified. Thus, here is the answer to the square root of 39674 in its simplest form:

√ 39674 = √ 39674

Here are two different methods we used to determine why the square root of 39674 cannot be simplified.

1) To be able to simplify the square root of 39674, one of the factors of 39674 other than 1 must be a perfect square. The factors of 39674 are 1, 2, 83, 166, 239, 478, 19837, and 39674. Since none of these factors are perfect squares, the square root of 39674 cannot be simplified.

2) To be able to simplify the square root of 39674, all the prime factors of 39674 cannot be unique. When we did prime factorization of 39674, we found that 2 x 83 x 239 equals 39674. Since all the prime factors are unique, the square root of 39674 cannot be simplified.

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