Simplify Square Root of 15509

What is the square root of 15509 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.

√15509 = A√B

Unfortunately, the square root of 15509 cannot be simplified. Thus, here is the answer to the square root of 15509 in its simplest form:

√ 15509 = √ 15509

Here are two different methods we used to determine why the square root of 15509 cannot be simplified.

1) To be able to simplify the square root of 15509, one of the factors of 15509 other than 1 must be a perfect square. The factors of 15509 are 1, 13, 1193, and 15509. Since none of these factors are perfect squares, the square root of 15509 cannot be simplified.

2) To be able to simplify the square root of 15509, all the prime factors of 15509 cannot be unique. When we did prime factorization of 15509, we found that 13 x 1193 equals 15509. Since all the prime factors are unique, the square root of 15509 cannot be simplified.

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