Simplify Square Root of 22667

What is the square root of 22667 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.

√22667 = A√B

Unfortunately, the square root of 22667 cannot be simplified. Thus, here is the answer to the square root of 22667 in its simplest form:

√ 22667 = √ 22667

Here are two different methods we used to determine why the square root of 22667 cannot be simplified.

1) To be able to simplify the square root of 22667, one of the factors of 22667 other than 1 must be a perfect square. The factors of 22667 are 1, 19, 1193, and 22667. Since none of these factors are perfect squares, the square root of 22667 cannot be simplified.

2) To be able to simplify the square root of 22667, all the prime factors of 22667 cannot be unique. When we did prime factorization of 22667, we found that 19 x 1193 equals 22667. Since all the prime factors are unique, the square root of 22667 cannot be simplified.

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