Simplify Square Root of 40126

What is the square root of 40126 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.

√40126 = A√B

Unfortunately, the square root of 40126 cannot be simplified. Thus, here is the answer to the square root of 40126 in its simplest form:

√ 40126 = √ 40126

Here are two different methods we used to determine why the square root of 40126 cannot be simplified.

1) To be able to simplify the square root of 40126, one of the factors of 40126 other than 1 must be a perfect square. The factors of 40126 are 1, 2, 20063, and 40126. Since none of these factors are perfect squares, the square root of 40126 cannot be simplified.

2) To be able to simplify the square root of 40126, all the prime factors of 40126 cannot be unique. When we did prime factorization of 40126, we found that 2 x 20063 equals 40126. Since all the prime factors are unique, the square root of 40126 cannot be simplified.

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