Simplify Square Root of 37790

What is the square root of 37790 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.

√37790 = A√B

Unfortunately, the square root of 37790 cannot be simplified. Thus, here is the answer to the square root of 37790 in its simplest form:

√ 37790 = √ 37790

Here are two different methods we used to determine why the square root of 37790 cannot be simplified.

1) To be able to simplify the square root of 37790, one of the factors of 37790 other than 1 must be a perfect square. The factors of 37790 are 1, 2, 5, 10, 3779, 7558, 18895, and 37790. Since none of these factors are perfect squares, the square root of 37790 cannot be simplified.

2) To be able to simplify the square root of 37790, all the prime factors of 37790 cannot be unique. When we did prime factorization of 37790, we found that 2 x 5 x 3779 equals 37790. Since all the prime factors are unique, the square root of 37790 cannot be simplified.

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