Simplify Square Root of 22569

What is the square root of 22569 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.

√22569 = A√B

Unfortunately, the square root of 22569 cannot be simplified. Thus, here is the answer to the square root of 22569 in its simplest form:

√ 22569 = √ 22569

Here are two different methods we used to determine why the square root of 22569 cannot be simplified.

1) To be able to simplify the square root of 22569, one of the factors of 22569 other than 1 must be a perfect square. The factors of 22569 are 1, 3, 7523, and 22569. Since none of these factors are perfect squares, the square root of 22569 cannot be simplified.

2) To be able to simplify the square root of 22569, all the prime factors of 22569 cannot be unique. When we did prime factorization of 22569, we found that 3 x 7523 equals 22569. Since all the prime factors are unique, the square root of 22569 cannot be simplified.

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