Simplify Square Root of 6274

What is the square root of 6274 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.

√6274 = A√B

Unfortunately, the square root of 6274 cannot be simplified. Thus, here is the answer to the square root of 6274 in its simplest form:

√ 6274 = √ 6274

Here are two different methods we used to determine why the square root of 6274 cannot be simplified.

1) To be able to simplify the square root of 6274, one of the factors of 6274 other than 1 must be a perfect square. The factors of 6274 are 1, 2, 3137, and 6274. Since none of these factors are perfect squares, the square root of 6274 cannot be simplified.

2) To be able to simplify the square root of 6274, all the prime factors of 6274 cannot be unique. When we did prime factorization of 6274, we found that 2 x 3137 equals 6274. Since all the prime factors are unique, the square root of 6274 cannot be simplified.

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