Simplify Square Root of 28166

What is the square root of 28166 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.

√28166 = A√B

Unfortunately, the square root of 28166 cannot be simplified. Thus, here is the answer to the square root of 28166 in its simplest form:

√ 28166 = √ 28166

Here are two different methods we used to determine why the square root of 28166 cannot be simplified.

1) To be able to simplify the square root of 28166, one of the factors of 28166 other than 1 must be a perfect square. The factors of 28166 are 1, 2, 14083, and 28166. Since none of these factors are perfect squares, the square root of 28166 cannot be simplified.

2) To be able to simplify the square root of 28166, all the prime factors of 28166 cannot be unique. When we did prime factorization of 28166, we found that 2 x 14083 equals 28166. Since all the prime factors are unique, the square root of 28166 cannot be simplified.

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