Simplify Square Root of 15734

What is the square root of 15734 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.

√15734 = A√B

Unfortunately, the square root of 15734 cannot be simplified. Thus, here is the answer to the square root of 15734 in its simplest form:

√ 15734 = √ 15734

Here are two different methods we used to determine why the square root of 15734 cannot be simplified.

1) To be able to simplify the square root of 15734, one of the factors of 15734 other than 1 must be a perfect square. The factors of 15734 are 1, 2, 7867, and 15734. Since none of these factors are perfect squares, the square root of 15734 cannot be simplified.

2) To be able to simplify the square root of 15734, all the prime factors of 15734 cannot be unique. When we did prime factorization of 15734, we found that 2 x 7867 equals 15734. Since all the prime factors are unique, the square root of 15734 cannot be simplified.

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