Simplify Square Root of 65509

What is the square root of 65509 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.

√65509 = A√B

Unfortunately, the square root of 65509 cannot be simplified. Thus, here is the answer to the square root of 65509 in its simplest form:

√ 65509 = √ 65509

Here are two different methods we used to determine why the square root of 65509 cannot be simplified.

1) To be able to simplify the square root of 65509, one of the factors of 65509 other than 1 must be a perfect square. The factors of 65509 are 1, 109, 601, and 65509. Since none of these factors are perfect squares, the square root of 65509 cannot be simplified.

2) To be able to simplify the square root of 65509, all the prime factors of 65509 cannot be unique. When we did prime factorization of 65509, we found that 109 x 601 equals 65509. Since all the prime factors are unique, the square root of 65509 cannot be simplified.

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