Simplify Square Root of 66651

What is the square root of 66651 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.

√66651 = A√B

Unfortunately, the square root of 66651 cannot be simplified. Thus, here is the answer to the square root of 66651 in its simplest form:

√ 66651 = √ 66651

Here are two different methods we used to determine why the square root of 66651 cannot be simplified.

1) To be able to simplify the square root of 66651, one of the factors of 66651 other than 1 must be a perfect square. The factors of 66651 are 1, 3, 13, 39, 1709, 5127, 22217, and 66651. Since none of these factors are perfect squares, the square root of 66651 cannot be simplified.

2) To be able to simplify the square root of 66651, all the prime factors of 66651 cannot be unique. When we did prime factorization of 66651, we found that 3 x 13 x 1709 equals 66651. Since all the prime factors are unique, the square root of 66651 cannot be simplified.

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