Simplify Square Root of 41421

What is the square root of 41421 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.

√41421 = A√B

Unfortunately, the square root of 41421 cannot be simplified. Thus, here is the answer to the square root of 41421 in its simplest form:

√ 41421 = √ 41421

Here are two different methods we used to determine why the square root of 41421 cannot be simplified.

1) To be able to simplify the square root of 41421, one of the factors of 41421 other than 1 must be a perfect square. The factors of 41421 are 1, 3, 13807, and 41421. Since none of these factors are perfect squares, the square root of 41421 cannot be simplified.

2) To be able to simplify the square root of 41421, all the prime factors of 41421 cannot be unique. When we did prime factorization of 41421, we found that 3 x 13807 equals 41421. Since all the prime factors are unique, the square root of 41421 cannot be simplified.

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