Simplify Square Root of 74666

What is the square root of 74666 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.

√74666 = A√B

Unfortunately, the square root of 74666 cannot be simplified. Thus, here is the answer to the square root of 74666 in its simplest form:

√ 74666 = √ 74666

Here are two different methods we used to determine why the square root of 74666 cannot be simplified.

1) To be able to simplify the square root of 74666, one of the factors of 74666 other than 1 must be a perfect square. The factors of 74666 are 1, 2, 37, 74, 1009, 2018, 37333, and 74666. Since none of these factors are perfect squares, the square root of 74666 cannot be simplified.

2) To be able to simplify the square root of 74666, all the prime factors of 74666 cannot be unique. When we did prime factorization of 74666, we found that 2 x 37 x 1009 equals 74666. Since all the prime factors are unique, the square root of 74666 cannot be simplified.

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