Simplify Square Root of 23083

What is the square root of 23083 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.

√23083 = A√B

Unfortunately, the square root of 23083 cannot be simplified. Thus, here is the answer to the square root of 23083 in its simplest form:

√ 23083 = √ 23083

Here are two different methods we used to determine why the square root of 23083 cannot be simplified.

1) To be able to simplify the square root of 23083, one of the factors of 23083 other than 1 must be a perfect square. The factors of 23083 are 1, 41, 563, and 23083. Since none of these factors are perfect squares, the square root of 23083 cannot be simplified.

2) To be able to simplify the square root of 23083, all the prime factors of 23083 cannot be unique. When we did prime factorization of 23083, we found that 41 x 563 equals 23083. Since all the prime factors are unique, the square root of 23083 cannot be simplified.

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