Simplify Square Root of 41590

What is the square root of 41590 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.

√41590 = A√B

Unfortunately, the square root of 41590 cannot be simplified. Thus, here is the answer to the square root of 41590 in its simplest form:

√ 41590 = √ 41590

Here are two different methods we used to determine why the square root of 41590 cannot be simplified.

1) To be able to simplify the square root of 41590, one of the factors of 41590 other than 1 must be a perfect square. The factors of 41590 are 1, 2, 5, 10, 4159, 8318, 20795, and 41590. Since none of these factors are perfect squares, the square root of 41590 cannot be simplified.

2) To be able to simplify the square root of 41590, all the prime factors of 41590 cannot be unique. When we did prime factorization of 41590, we found that 2 x 5 x 4159 equals 41590. Since all the prime factors are unique, the square root of 41590 cannot be simplified.

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