Simplify Square Root of 42585

What is the square root of 42585 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.

√42585 = A√B

Unfortunately, the square root of 42585 cannot be simplified. Thus, here is the answer to the square root of 42585 in its simplest form:

√ 42585 = √ 42585

Here are two different methods we used to determine why the square root of 42585 cannot be simplified.

1) To be able to simplify the square root of 42585, one of the factors of 42585 other than 1 must be a perfect square. The factors of 42585 are 1, 3, 5, 15, 17, 51, 85, 167, 255, 501, 835, 2505, 2839, 8517, 14195, and 42585. Since none of these factors are perfect squares, the square root of 42585 cannot be simplified.

2) To be able to simplify the square root of 42585, all the prime factors of 42585 cannot be unique. When we did prime factorization of 42585, we found that 3 x 5 x 17 x 167 equals 42585. Since all the prime factors are unique, the square root of 42585 cannot be simplified.

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