Simplify Square Root of 38509

What is the square root of 38509 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.

√38509 = A√B

Unfortunately, the square root of 38509 cannot be simplified. Thus, here is the answer to the square root of 38509 in its simplest form:

√ 38509 = √ 38509

Here are two different methods we used to determine why the square root of 38509 cannot be simplified.

1) To be able to simplify the square root of 38509, one of the factors of 38509 other than 1 must be a perfect square. The factors of 38509 are 1, 97, 397, and 38509. Since none of these factors are perfect squares, the square root of 38509 cannot be simplified.

2) To be able to simplify the square root of 38509, all the prime factors of 38509 cannot be unique. When we did prime factorization of 38509, we found that 97 x 397 equals 38509. Since all the prime factors are unique, the square root of 38509 cannot be simplified.

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