Simplify Square Root of 25014

What is the square root of 25014 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.

√25014 = A√B

Unfortunately, the square root of 25014 cannot be simplified. Thus, here is the answer to the square root of 25014 in its simplest form:

√ 25014 = √ 25014

Here are two different methods we used to determine why the square root of 25014 cannot be simplified.

1) To be able to simplify the square root of 25014, one of the factors of 25014 other than 1 must be a perfect square. The factors of 25014 are 1, 2, 3, 6, 11, 22, 33, 66, 379, 758, 1137, 2274, 4169, 8338, 12507, and 25014. Since none of these factors are perfect squares, the square root of 25014 cannot be simplified.

2) To be able to simplify the square root of 25014, all the prime factors of 25014 cannot be unique. When we did prime factorization of 25014, we found that 2 x 3 x 11 x 379 equals 25014. Since all the prime factors are unique, the square root of 25014 cannot be simplified.

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