Simplify Square Root of 713

What is the square root of 713 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.

√713 = A√B

Unfortunately, the square root of 713 cannot be simplified. Thus, here is the answer to the square root of 713 in its simplest form:

√ 713 = √ 713

Here are two different methods we used to determine why the square root of 713 cannot be simplified.

1) To be able to simplify the square root of 713, one of the factors of 713 other than 1 must be a perfect square. The factors of 713 are 1, 23, 31, and 713. Since none of these factors are perfect squares, the square root of 713 cannot be simplified.

2) To be able to simplify the square root of 713, all the prime factors of 713 cannot be unique. When we did prime factorization of 713, we found that 23 x 31 equals 713. Since all the prime factors are unique, the square root of 713 cannot be simplified.

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