Simplify Square Root of 54861

What is the square root of 54861 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.

√54861 = A√B

Unfortunately, the square root of 54861 cannot be simplified. Thus, here is the answer to the square root of 54861 in its simplest form:

√ 54861 = √ 54861

Here are two different methods we used to determine why the square root of 54861 cannot be simplified.

1) To be able to simplify the square root of 54861, one of the factors of 54861 other than 1 must be a perfect square. The factors of 54861 are 1, 3, 18287, and 54861. Since none of these factors are perfect squares, the square root of 54861 cannot be simplified.

2) To be able to simplify the square root of 54861, all the prime factors of 54861 cannot be unique. When we did prime factorization of 54861, we found that 3 x 18287 equals 54861. Since all the prime factors are unique, the square root of 54861 cannot be simplified.

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