Simplify Square Root of 65209

What is the square root of 65209 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.

√65209 = A√B

Unfortunately, the square root of 65209 cannot be simplified. Thus, here is the answer to the square root of 65209 in its simplest form:

√ 65209 = √ 65209

Here are two different methods we used to determine why the square root of 65209 cannot be simplified.

1) To be able to simplify the square root of 65209, one of the factors of 65209 other than 1 must be a perfect square. The factors of 65209 are 1, 61, 1069, and 65209. Since none of these factors are perfect squares, the square root of 65209 cannot be simplified.

2) To be able to simplify the square root of 65209, all the prime factors of 65209 cannot be unique. When we did prime factorization of 65209, we found that 61 x 1069 equals 65209. Since all the prime factors are unique, the square root of 65209 cannot be simplified.

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