Simplify Square Root of 9683

What is the square root of 9683 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.

√9683 = A√B

Unfortunately, the square root of 9683 cannot be simplified. Thus, here is the answer to the square root of 9683 in its simplest form:

√ 9683 = √ 9683

Here are two different methods we used to determine why the square root of 9683 cannot be simplified.

1) To be able to simplify the square root of 9683, one of the factors of 9683 other than 1 must be a perfect square. The factors of 9683 are 1, 23, 421, and 9683. Since none of these factors are perfect squares, the square root of 9683 cannot be simplified.

2) To be able to simplify the square root of 9683, all the prime factors of 9683 cannot be unique. When we did prime factorization of 9683, we found that 23 x 421 equals 9683. Since all the prime factors are unique, the square root of 9683 cannot be simplified.

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