Simplify Square Root of 49313

What is the square root of 49313 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.

√49313 = A√B

Unfortunately, the square root of 49313 cannot be simplified. Thus, here is the answer to the square root of 49313 in its simplest form:

√ 49313 = √ 49313

Here are two different methods we used to determine why the square root of 49313 cannot be simplified.

1) To be able to simplify the square root of 49313, one of the factors of 49313 other than 1 must be a perfect square. The factors of 49313 are 1, 11, 4483, and 49313. Since none of these factors are perfect squares, the square root of 49313 cannot be simplified.

2) To be able to simplify the square root of 49313, all the prime factors of 49313 cannot be unique. When we did prime factorization of 49313, we found that 11 x 4483 equals 49313. Since all the prime factors are unique, the square root of 49313 cannot be simplified.

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