Simplify Square Root of 81583

What is the square root of 81583 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.

√81583 = A√B

Unfortunately, the square root of 81583 cannot be simplified. Thus, here is the answer to the square root of 81583 in its simplest form:

√ 81583 = √ 81583

Here are two different methods we used to determine why the square root of 81583 cannot be simplified.

1) To be able to simplify the square root of 81583, one of the factors of 81583 other than 1 must be a perfect square. The factors of 81583 are 1, 17, 4799, and 81583. Since none of these factors are perfect squares, the square root of 81583 cannot be simplified.

2) To be able to simplify the square root of 81583, all the prime factors of 81583 cannot be unique. When we did prime factorization of 81583, we found that 17 x 4799 equals 81583. Since all the prime factors are unique, the square root of 81583 cannot be simplified.

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