Simplify Square Root of 22377

What is the square root of 22377 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.

√22377 = A√B

Unfortunately, the square root of 22377 cannot be simplified. Thus, here is the answer to the square root of 22377 in its simplest form:

√ 22377 = √ 22377

Here are two different methods we used to determine why the square root of 22377 cannot be simplified.

1) To be able to simplify the square root of 22377, one of the factors of 22377 other than 1 must be a perfect square. The factors of 22377 are 1, 3, 7459, and 22377. Since none of these factors are perfect squares, the square root of 22377 cannot be simplified.

2) To be able to simplify the square root of 22377, all the prime factors of 22377 cannot be unique. When we did prime factorization of 22377, we found that 3 x 7459 equals 22377. Since all the prime factors are unique, the square root of 22377 cannot be simplified.

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