Simplify Square Root of 44666

What is the square root of 44666 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.

√44666 = A√B

Unfortunately, the square root of 44666 cannot be simplified. Thus, here is the answer to the square root of 44666 in its simplest form:

√ 44666 = √ 44666

Here are two different methods we used to determine why the square root of 44666 cannot be simplified.

1) To be able to simplify the square root of 44666, one of the factors of 44666 other than 1 must be a perfect square. The factors of 44666 are 1, 2, 23, 46, 971, 1942, 22333, and 44666. Since none of these factors are perfect squares, the square root of 44666 cannot be simplified.

2) To be able to simplify the square root of 44666, all the prime factors of 44666 cannot be unique. When we did prime factorization of 44666, we found that 2 x 23 x 971 equals 44666. Since all the prime factors are unique, the square root of 44666 cannot be simplified.

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