Simplify Square Root of 731

What is the square root of 731 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.

√731 = A√B

Unfortunately, the square root of 731 cannot be simplified. Thus, here is the answer to the square root of 731 in its simplest form:

√ 731 = √ 731

Here are two different methods we used to determine why the square root of 731 cannot be simplified.

1) To be able to simplify the square root of 731, one of the factors of 731 other than 1 must be a perfect square. The factors of 731 are 1, 17, 43, and 731. Since none of these factors are perfect squares, the square root of 731 cannot be simplified.

2) To be able to simplify the square root of 731, all the prime factors of 731 cannot be unique. When we did prime factorization of 731, we found that 17 x 43 equals 731. Since all the prime factors are unique, the square root of 731 cannot be simplified.

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