Simplify Square Root of 4866

What is the square root of 4866 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.

√4866 = A√B

Unfortunately, the square root of 4866 cannot be simplified. Thus, here is the answer to the square root of 4866 in its simplest form:

√ 4866 = √ 4866

Here are two different methods we used to determine why the square root of 4866 cannot be simplified.

1) To be able to simplify the square root of 4866, one of the factors of 4866 other than 1 must be a perfect square. The factors of 4866 are 1, 2, 3, 6, 811, 1622, 2433, and 4866. Since none of these factors are perfect squares, the square root of 4866 cannot be simplified.

2) To be able to simplify the square root of 4866, all the prime factors of 4866 cannot be unique. When we did prime factorization of 4866, we found that 2 x 3 x 811 equals 4866. Since all the prime factors are unique, the square root of 4866 cannot be simplified.

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