Simplify Square Root of 614

What is the square root of 614 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.

√614 = A√B

Unfortunately, the square root of 614 cannot be simplified. Thus, here is the answer to the square root of 614 in its simplest form:

√ 614 = √ 614

Here are two different methods we used to determine why the square root of 614 cannot be simplified.

1) To be able to simplify the square root of 614, one of the factors of 614 other than 1 must be a perfect square. The factors of 614 are 1, 2, 307, and 614. Since none of these factors are perfect squares, the square root of 614 cannot be simplified.

2) To be able to simplify the square root of 614, all the prime factors of 614 cannot be unique. When we did prime factorization of 614, we found that 2 x 307 equals 614. Since all the prime factors are unique, the square root of 614 cannot be simplified.

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