Simplify Square Root of 81623

What is the square root of 81623 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.

√81623 = A√B

Unfortunately, the square root of 81623 cannot be simplified. Thus, here is the answer to the square root of 81623 in its simplest form:

√ 81623 = √ 81623

Here are two different methods we used to determine why the square root of 81623 cannot be simplified.

1) To be able to simplify the square root of 81623, one of the factors of 81623 other than 1 must be a perfect square. The factors of 81623 are 1, 31, 2633, and 81623. Since none of these factors are perfect squares, the square root of 81623 cannot be simplified.

2) To be able to simplify the square root of 81623, all the prime factors of 81623 cannot be unique. When we did prime factorization of 81623, we found that 31 x 2633 equals 81623. Since all the prime factors are unique, the square root of 81623 cannot be simplified.

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