Simplify Square Root of 38814

What is the square root of 38814 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.

√38814 = A√B

Unfortunately, the square root of 38814 cannot be simplified. Thus, here is the answer to the square root of 38814 in its simplest form:

√ 38814 = √ 38814

Here are two different methods we used to determine why the square root of 38814 cannot be simplified.

1) To be able to simplify the square root of 38814, one of the factors of 38814 other than 1 must be a perfect square. The factors of 38814 are 1, 2, 3, 6, 6469, 12938, 19407, and 38814. Since none of these factors are perfect squares, the square root of 38814 cannot be simplified.

2) To be able to simplify the square root of 38814, all the prime factors of 38814 cannot be unique. When we did prime factorization of 38814, we found that 2 x 3 x 6469 equals 38814. Since all the prime factors are unique, the square root of 38814 cannot be simplified.

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