Simplify Square Root of 40685

What is the square root of 40685 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.

√40685 = A√B

Unfortunately, the square root of 40685 cannot be simplified. Thus, here is the answer to the square root of 40685 in its simplest form:

√ 40685 = √ 40685

Here are two different methods we used to determine why the square root of 40685 cannot be simplified.

1) To be able to simplify the square root of 40685, one of the factors of 40685 other than 1 must be a perfect square. The factors of 40685 are 1, 5, 79, 103, 395, 515, 8137, and 40685. Since none of these factors are perfect squares, the square root of 40685 cannot be simplified.

2) To be able to simplify the square root of 40685, all the prime factors of 40685 cannot be unique. When we did prime factorization of 40685, we found that 5 x 79 x 103 equals 40685. Since all the prime factors are unique, the square root of 40685 cannot be simplified.

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