Simplify Square Root of 37091

What is the square root of 37091 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.

√37091 = A√B

Unfortunately, the square root of 37091 cannot be simplified. Thus, here is the answer to the square root of 37091 in its simplest form:

√ 37091 = √ 37091

Here are two different methods we used to determine why the square root of 37091 cannot be simplified.

1) To be able to simplify the square root of 37091, one of the factors of 37091 other than 1 must be a perfect square. The factors of 37091 are 1, 29, 1279, and 37091. Since none of these factors are perfect squares, the square root of 37091 cannot be simplified.

2) To be able to simplify the square root of 37091, all the prime factors of 37091 cannot be unique. When we did prime factorization of 37091, we found that 29 x 1279 equals 37091. Since all the prime factors are unique, the square root of 37091 cannot be simplified.

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