Simplify Square Root of 38254

What is the square root of 38254 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.

√38254 = A√B

Unfortunately, the square root of 38254 cannot be simplified. Thus, here is the answer to the square root of 38254 in its simplest form:

√ 38254 = √ 38254

Here are two different methods we used to determine why the square root of 38254 cannot be simplified.

1) To be able to simplify the square root of 38254, one of the factors of 38254 other than 1 must be a perfect square. The factors of 38254 are 1, 2, 31, 62, 617, 1234, 19127, and 38254. Since none of these factors are perfect squares, the square root of 38254 cannot be simplified.

2) To be able to simplify the square root of 38254, all the prime factors of 38254 cannot be unique. When we did prime factorization of 38254, we found that 2 x 31 x 617 equals 38254. Since all the prime factors are unique, the square root of 38254 cannot be simplified.

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