Simplify Square Root of 37077

What is the square root of 37077 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.

√37077 = A√B

Unfortunately, the square root of 37077 cannot be simplified. Thus, here is the answer to the square root of 37077 in its simplest form:

√ 37077 = √ 37077

Here are two different methods we used to determine why the square root of 37077 cannot be simplified.

1) To be able to simplify the square root of 37077, one of the factors of 37077 other than 1 must be a perfect square. The factors of 37077 are 1, 3, 17, 51, 727, 2181, 12359, and 37077. Since none of these factors are perfect squares, the square root of 37077 cannot be simplified.

2) To be able to simplify the square root of 37077, all the prime factors of 37077 cannot be unique. When we did prime factorization of 37077, we found that 3 x 17 x 727 equals 37077. Since all the prime factors are unique, the square root of 37077 cannot be simplified.

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