Simplify Square Root of 45509

What is the square root of 45509 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.

√45509 = A√B

Unfortunately, the square root of 45509 cannot be simplified. Thus, here is the answer to the square root of 45509 in its simplest form:

√ 45509 = √ 45509

Here are two different methods we used to determine why the square root of 45509 cannot be simplified.

1) To be able to simplify the square root of 45509, one of the factors of 45509 other than 1 must be a perfect square. The factors of 45509 are 1, 17, 2677, and 45509. Since none of these factors are perfect squares, the square root of 45509 cannot be simplified.

2) To be able to simplify the square root of 45509, all the prime factors of 45509 cannot be unique. When we did prime factorization of 45509, we found that 17 x 2677 equals 45509. Since all the prime factors are unique, the square root of 45509 cannot be simplified.

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