Simplify Square Root of 41138

What is the square root of 41138 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.

√41138 = A√B

Unfortunately, the square root of 41138 cannot be simplified. Thus, here is the answer to the square root of 41138 in its simplest form:

√ 41138 = √ 41138

Here are two different methods we used to determine why the square root of 41138 cannot be simplified.

1) To be able to simplify the square root of 41138, one of the factors of 41138 other than 1 must be a perfect square. The factors of 41138 are 1, 2, 67, 134, 307, 614, 20569, and 41138. Since none of these factors are perfect squares, the square root of 41138 cannot be simplified.

2) To be able to simplify the square root of 41138, all the prime factors of 41138 cannot be unique. When we did prime factorization of 41138, we found that 2 x 67 x 307 equals 41138. Since all the prime factors are unique, the square root of 41138 cannot be simplified.

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