Simplify Square Root of 37819

What is the square root of 37819 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.

√37819 = A√B

Unfortunately, the square root of 37819 cannot be simplified. Thus, here is the answer to the square root of 37819 in its simplest form:

√ 37819 = √ 37819

Here are two different methods we used to determine why the square root of 37819 cannot be simplified.

1) To be able to simplify the square root of 37819, one of the factors of 37819 other than 1 must be a perfect square. The factors of 37819 are 1, 59, 641, and 37819. Since none of these factors are perfect squares, the square root of 37819 cannot be simplified.

2) To be able to simplify the square root of 37819, all the prime factors of 37819 cannot be unique. When we did prime factorization of 37819, we found that 59 x 641 equals 37819. Since all the prime factors are unique, the square root of 37819 cannot be simplified.

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