Simplify Square Root of 41834

What is the square root of 41834 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.

√41834 = A√B

Unfortunately, the square root of 41834 cannot be simplified. Thus, here is the answer to the square root of 41834 in its simplest form:

√ 41834 = √ 41834

Here are two different methods we used to determine why the square root of 41834 cannot be simplified.

1) To be able to simplify the square root of 41834, one of the factors of 41834 other than 1 must be a perfect square. The factors of 41834 are 1, 2, 13, 26, 1609, 3218, 20917, and 41834. Since none of these factors are perfect squares, the square root of 41834 cannot be simplified.

2) To be able to simplify the square root of 41834, all the prime factors of 41834 cannot be unique. When we did prime factorization of 41834, we found that 2 x 13 x 1609 equals 41834. Since all the prime factors are unique, the square root of 41834 cannot be simplified.

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