Simplify Square Root of 65593

What is the square root of 65593 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.

√65593 = A√B

Unfortunately, the square root of 65593 cannot be simplified. Thus, here is the answer to the square root of 65593 in its simplest form:

√ 65593 = √ 65593

Here are two different methods we used to determine why the square root of 65593 cannot be simplified.

1) To be able to simplify the square root of 65593, one of the factors of 65593 other than 1 must be a perfect square. The factors of 65593 are 1, 11, 67, 89, 737, 979, 5963, and 65593. Since none of these factors are perfect squares, the square root of 65593 cannot be simplified.

2) To be able to simplify the square root of 65593, all the prime factors of 65593 cannot be unique. When we did prime factorization of 65593, we found that 11 x 67 x 89 equals 65593. Since all the prime factors are unique, the square root of 65593 cannot be simplified.

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