Simplify Square Root of 37193

What is the square root of 37193 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.

√37193 = A√B

Unfortunately, the square root of 37193 cannot be simplified. Thus, here is the answer to the square root of 37193 in its simplest form:

√ 37193 = √ 37193

Here are two different methods we used to determine why the square root of 37193 cannot be simplified.

1) To be able to simplify the square root of 37193, one of the factors of 37193 other than 1 must be a perfect square. The factors of 37193 are 1, 13, 2861, and 37193. Since none of these factors are perfect squares, the square root of 37193 cannot be simplified.

2) To be able to simplify the square root of 37193, all the prime factors of 37193 cannot be unique. When we did prime factorization of 37193, we found that 13 x 2861 equals 37193. Since all the prime factors are unique, the square root of 37193 cannot be simplified.

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