Simplify Square Root of 41645

What is the square root of 41645 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.

√41645 = A√B

Unfortunately, the square root of 41645 cannot be simplified. Thus, here is the answer to the square root of 41645 in its simplest form:

√ 41645 = √ 41645

Here are two different methods we used to determine why the square root of 41645 cannot be simplified.

1) To be able to simplify the square root of 41645, one of the factors of 41645 other than 1 must be a perfect square. The factors of 41645 are 1, 5, 8329, and 41645. Since none of these factors are perfect squares, the square root of 41645 cannot be simplified.

2) To be able to simplify the square root of 41645, all the prime factors of 41645 cannot be unique. When we did prime factorization of 41645, we found that 5 x 8329 equals 41645. Since all the prime factors are unique, the square root of 41645 cannot be simplified.

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