Simplify Square Root of 38521

What is the square root of 38521 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.

√38521 = A√B

Unfortunately, the square root of 38521 cannot be simplified. Thus, here is the answer to the square root of 38521 in its simplest form:

√ 38521 = √ 38521

Here are two different methods we used to determine why the square root of 38521 cannot be simplified.

1) To be able to simplify the square root of 38521, one of the factors of 38521 other than 1 must be a perfect square. The factors of 38521 are 1, 7, 5503, and 38521. Since none of these factors are perfect squares, the square root of 38521 cannot be simplified.

2) To be able to simplify the square root of 38521, all the prime factors of 38521 cannot be unique. When we did prime factorization of 38521, we found that 7 x 5503 equals 38521. Since all the prime factors are unique, the square root of 38521 cannot be simplified.

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