Simplify Square Root of 42638

What is the square root of 42638 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.

√42638 = A√B

Unfortunately, the square root of 42638 cannot be simplified. Thus, here is the answer to the square root of 42638 in its simplest form:

√ 42638 = √ 42638

Here are two different methods we used to determine why the square root of 42638 cannot be simplified.

1) To be able to simplify the square root of 42638, one of the factors of 42638 other than 1 must be a perfect square. The factors of 42638 are 1, 2, 21319, and 42638. Since none of these factors are perfect squares, the square root of 42638 cannot be simplified.

2) To be able to simplify the square root of 42638, all the prime factors of 42638 cannot be unique. When we did prime factorization of 42638, we found that 2 x 21319 equals 42638. Since all the prime factors are unique, the square root of 42638 cannot be simplified.

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