Simplify Square Root of 49314

What is the square root of 49314 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.

√49314 = A√B

Unfortunately, the square root of 49314 cannot be simplified. Thus, here is the answer to the square root of 49314 in its simplest form:

√ 49314 = √ 49314

Here are two different methods we used to determine why the square root of 49314 cannot be simplified.

1) To be able to simplify the square root of 49314, one of the factors of 49314 other than 1 must be a perfect square. The factors of 49314 are 1, 2, 3, 6, 8219, 16438, 24657, and 49314. Since none of these factors are perfect squares, the square root of 49314 cannot be simplified.

2) To be able to simplify the square root of 49314, all the prime factors of 49314 cannot be unique. When we did prime factorization of 49314, we found that 2 x 3 x 8219 equals 49314. Since all the prime factors are unique, the square root of 49314 cannot be simplified.

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