Simplify Square Root of 81565

What is the square root of 81565 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.

√81565 = A√B

Unfortunately, the square root of 81565 cannot be simplified. Thus, here is the answer to the square root of 81565 in its simplest form:

√ 81565 = √ 81565

Here are two different methods we used to determine why the square root of 81565 cannot be simplified.

1) To be able to simplify the square root of 81565, one of the factors of 81565 other than 1 must be a perfect square. The factors of 81565 are 1, 5, 11, 55, 1483, 7415, 16313, and 81565. Since none of these factors are perfect squares, the square root of 81565 cannot be simplified.

2) To be able to simplify the square root of 81565, all the prime factors of 81565 cannot be unique. When we did prime factorization of 81565, we found that 5 x 11 x 1483 equals 81565. Since all the prime factors are unique, the square root of 81565 cannot be simplified.

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