Simplify Square Root of 22614

What is the square root of 22614 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.

√22614 = A√B

Unfortunately, the square root of 22614 cannot be simplified. Thus, here is the answer to the square root of 22614 in its simplest form:

√ 22614 = √ 22614

Here are two different methods we used to determine why the square root of 22614 cannot be simplified.

1) To be able to simplify the square root of 22614, one of the factors of 22614 other than 1 must be a perfect square. The factors of 22614 are 1, 2, 3, 6, 3769, 7538, 11307, and 22614. Since none of these factors are perfect squares, the square root of 22614 cannot be simplified.

2) To be able to simplify the square root of 22614, all the prime factors of 22614 cannot be unique. When we did prime factorization of 22614, we found that 2 x 3 x 3769 equals 22614. Since all the prime factors are unique, the square root of 22614 cannot be simplified.

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