Simplify Square Root of 22823

What is the square root of 22823 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.

√22823 = A√B

Unfortunately, the square root of 22823 cannot be simplified. Thus, here is the answer to the square root of 22823 in its simplest form:

√ 22823 = √ 22823

Here are two different methods we used to determine why the square root of 22823 cannot be simplified.

1) To be able to simplify the square root of 22823, one of the factors of 22823 other than 1 must be a perfect square. The factors of 22823 are 1, 29, 787, and 22823. Since none of these factors are perfect squares, the square root of 22823 cannot be simplified.

2) To be able to simplify the square root of 22823, all the prime factors of 22823 cannot be unique. When we did prime factorization of 22823, we found that 29 x 787 equals 22823. Since all the prime factors are unique, the square root of 22823 cannot be simplified.

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