Simplify Square Root of 23178

What is the square root of 23178 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.

√23178 = A√B

Unfortunately, the square root of 23178 cannot be simplified. Thus, here is the answer to the square root of 23178 in its simplest form:

√ 23178 = √ 23178

Here are two different methods we used to determine why the square root of 23178 cannot be simplified.

1) To be able to simplify the square root of 23178, one of the factors of 23178 other than 1 must be a perfect square. The factors of 23178 are 1, 2, 3, 6, 3863, 7726, 11589, and 23178. Since none of these factors are perfect squares, the square root of 23178 cannot be simplified.

2) To be able to simplify the square root of 23178, all the prime factors of 23178 cannot be unique. When we did prime factorization of 23178, we found that 2 x 3 x 3863 equals 23178. Since all the prime factors are unique, the square root of 23178 cannot be simplified.

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