Simplify Square Root of 42378

What is the square root of 42378 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.

√42378 = A√B

Unfortunately, the square root of 42378 cannot be simplified. Thus, here is the answer to the square root of 42378 in its simplest form:

√ 42378 = √ 42378

Here are two different methods we used to determine why the square root of 42378 cannot be simplified.

1) To be able to simplify the square root of 42378, one of the factors of 42378 other than 1 must be a perfect square. The factors of 42378 are 1, 2, 3, 6, 7, 14, 21, 42, 1009, 2018, 3027, 6054, 7063, 14126, 21189, and 42378. Since none of these factors are perfect squares, the square root of 42378 cannot be simplified.

2) To be able to simplify the square root of 42378, all the prime factors of 42378 cannot be unique. When we did prime factorization of 42378, we found that 2 x 3 x 7 x 1009 equals 42378. Since all the prime factors are unique, the square root of 42378 cannot be simplified.

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