Simplify Square Root of 23583

What is the square root of 23583 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.

√23583 = A√B

Unfortunately, the square root of 23583 cannot be simplified. Thus, here is the answer to the square root of 23583 in its simplest form:

√ 23583 = √ 23583

Here are two different methods we used to determine why the square root of 23583 cannot be simplified.

1) To be able to simplify the square root of 23583, one of the factors of 23583 other than 1 must be a perfect square. The factors of 23583 are 1, 3, 7, 21, 1123, 3369, 7861, and 23583. Since none of these factors are perfect squares, the square root of 23583 cannot be simplified.

2) To be able to simplify the square root of 23583, all the prime factors of 23583 cannot be unique. When we did prime factorization of 23583, we found that 3 x 7 x 1123 equals 23583. Since all the prime factors are unique, the square root of 23583 cannot be simplified.

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