Simplify Square Root of 25006

What is the square root of 25006 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.

√25006 = A√B

Unfortunately, the square root of 25006 cannot be simplified. Thus, here is the answer to the square root of 25006 in its simplest form:

√ 25006 = √ 25006

Here are two different methods we used to determine why the square root of 25006 cannot be simplified.

1) To be able to simplify the square root of 25006, one of the factors of 25006 other than 1 must be a perfect square. The factors of 25006 are 1, 2, 12503, and 25006. Since none of these factors are perfect squares, the square root of 25006 cannot be simplified.

2) To be able to simplify the square root of 25006, all the prime factors of 25006 cannot be unique. When we did prime factorization of 25006, we found that 2 x 12503 equals 25006. Since all the prime factors are unique, the square root of 25006 cannot be simplified.

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