Simplify Square Root of 37626

What is the square root of 37626 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.

√37626 = A√B

Unfortunately, the square root of 37626 cannot be simplified. Thus, here is the answer to the square root of 37626 in its simplest form:

√ 37626 = √ 37626

Here are two different methods we used to determine why the square root of 37626 cannot be simplified.

1) To be able to simplify the square root of 37626, one of the factors of 37626 other than 1 must be a perfect square. The factors of 37626 are 1, 2, 3, 6, 6271, 12542, 18813, and 37626. Since none of these factors are perfect squares, the square root of 37626 cannot be simplified.

2) To be able to simplify the square root of 37626, all the prime factors of 37626 cannot be unique. When we did prime factorization of 37626, we found that 2 x 3 x 6271 equals 37626. Since all the prime factors are unique, the square root of 37626 cannot be simplified.

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