Simplify Square Root of 22174

What is the square root of 22174 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.

√22174 = A√B

Unfortunately, the square root of 22174 cannot be simplified. Thus, here is the answer to the square root of 22174 in its simplest form:

√ 22174 = √ 22174

Here are two different methods we used to determine why the square root of 22174 cannot be simplified.

1) To be able to simplify the square root of 22174, one of the factors of 22174 other than 1 must be a perfect square. The factors of 22174 are 1, 2, 11087, and 22174. Since none of these factors are perfect squares, the square root of 22174 cannot be simplified.

2) To be able to simplify the square root of 22174, all the prime factors of 22174 cannot be unique. When we did prime factorization of 22174, we found that 2 x 11087 equals 22174. Since all the prime factors are unique, the square root of 22174 cannot be simplified.

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