Simplify Square Root of 45166

What is the square root of 45166 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.

√45166 = A√B

Unfortunately, the square root of 45166 cannot be simplified. Thus, here is the answer to the square root of 45166 in its simplest form:

√ 45166 = √ 45166

Here are two different methods we used to determine why the square root of 45166 cannot be simplified.

1) To be able to simplify the square root of 45166, one of the factors of 45166 other than 1 must be a perfect square. The factors of 45166 are 1, 2, 11, 22, 2053, 4106, 22583, and 45166. Since none of these factors are perfect squares, the square root of 45166 cannot be simplified.

2) To be able to simplify the square root of 45166, all the prime factors of 45166 cannot be unique. When we did prime factorization of 45166, we found that 2 x 11 x 2053 equals 45166. Since all the prime factors are unique, the square root of 45166 cannot be simplified.

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