Simplify Square Root of 23757

What is the square root of 23757 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.

√23757 = A√B

Unfortunately, the square root of 23757 cannot be simplified. Thus, here is the answer to the square root of 23757 in its simplest form:

√ 23757 = √ 23757

Here are two different methods we used to determine why the square root of 23757 cannot be simplified.

1) To be able to simplify the square root of 23757, one of the factors of 23757 other than 1 must be a perfect square. The factors of 23757 are 1, 3, 7919, and 23757. Since none of these factors are perfect squares, the square root of 23757 cannot be simplified.

2) To be able to simplify the square root of 23757, all the prime factors of 23757 cannot be unique. When we did prime factorization of 23757, we found that 3 x 7919 equals 23757. Since all the prime factors are unique, the square root of 23757 cannot be simplified.

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