Simplify Square Root of 9678

What is the square root of 9678 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.

√9678 = A√B

Unfortunately, the square root of 9678 cannot be simplified. Thus, here is the answer to the square root of 9678 in its simplest form:

√ 9678 = √ 9678

Here are two different methods we used to determine why the square root of 9678 cannot be simplified.

1) To be able to simplify the square root of 9678, one of the factors of 9678 other than 1 must be a perfect square. The factors of 9678 are 1, 2, 3, 6, 1613, 3226, 4839, and 9678. Since none of these factors are perfect squares, the square root of 9678 cannot be simplified.

2) To be able to simplify the square root of 9678, all the prime factors of 9678 cannot be unique. When we did prime factorization of 9678, we found that 2 x 3 x 1613 equals 9678. Since all the prime factors are unique, the square root of 9678 cannot be simplified.

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