Simplify Square Root of 40466

What is the square root of 40466 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.

√40466 = A√B

Unfortunately, the square root of 40466 cannot be simplified. Thus, here is the answer to the square root of 40466 in its simplest form:

√ 40466 = √ 40466

Here are two different methods we used to determine why the square root of 40466 cannot be simplified.

1) To be able to simplify the square root of 40466, one of the factors of 40466 other than 1 must be a perfect square. The factors of 40466 are 1, 2, 20233, and 40466. Since none of these factors are perfect squares, the square root of 40466 cannot be simplified.

2) To be able to simplify the square root of 40466, all the prime factors of 40466 cannot be unique. When we did prime factorization of 40466, we found that 2 x 20233 equals 40466. Since all the prime factors are unique, the square root of 40466 cannot be simplified.

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