Simplify Square Root of 313

What is the square root of 313 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.

√313 = A√B

Unfortunately, the square root of 313 cannot be simplified. Thus, here is the answer to the square root of 313 in its simplest form:

√ 313 = √ 313

Here are two different methods we used to determine why the square root of 313 cannot be simplified.

1) To be able to simplify the square root of 313, one of the factors of 313 other than 1 must be a perfect square. The factors of 313 are 1 and 313. Since none of these factors are perfect squares, the square root of 313 cannot be simplified.

2) To be able to simplify the square root of 313, all the prime factors of 313 cannot be unique. When we did prime factorization of 313, we found that 313 equals 313. Since all the prime factors are unique, the square root of 313 cannot be simplified.

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Simplify Square Root of 314
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