Simplify Square Root of 40951

What is the square root of 40951 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.

√40951 = A√B

Unfortunately, the square root of 40951 cannot be simplified. Thus, here is the answer to the square root of 40951 in its simplest form:

√ 40951 = √ 40951

Here are two different methods we used to determine why the square root of 40951 cannot be simplified.

1) To be able to simplify the square root of 40951, one of the factors of 40951 other than 1 must be a perfect square. The factors of 40951 are 1, 31, 1321, and 40951. Since none of these factors are perfect squares, the square root of 40951 cannot be simplified.

2) To be able to simplify the square root of 40951, all the prime factors of 40951 cannot be unique. When we did prime factorization of 40951, we found that 31 x 1321 equals 40951. Since all the prime factors are unique, the square root of 40951 cannot be simplified.

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