Simplify Square Root of 42566

What is the square root of 42566 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.

√42566 = A√B

Unfortunately, the square root of 42566 cannot be simplified. Thus, here is the answer to the square root of 42566 in its simplest form:

√ 42566 = √ 42566

Here are two different methods we used to determine why the square root of 42566 cannot be simplified.

1) To be able to simplify the square root of 42566, one of the factors of 42566 other than 1 must be a perfect square. The factors of 42566 are 1, 2, 21283, and 42566. Since none of these factors are perfect squares, the square root of 42566 cannot be simplified.

2) To be able to simplify the square root of 42566, all the prime factors of 42566 cannot be unique. When we did prime factorization of 42566, we found that 2 x 21283 equals 42566. Since all the prime factors are unique, the square root of 42566 cannot be simplified.

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