Simplify Square Root of 7842

What is the square root of 7842 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.

√7842 = A√B

Unfortunately, the square root of 7842 cannot be simplified. Thus, here is the answer to the square root of 7842 in its simplest form:

√ 7842 = √ 7842

Here are two different methods we used to determine why the square root of 7842 cannot be simplified.

1) To be able to simplify the square root of 7842, one of the factors of 7842 other than 1 must be a perfect square. The factors of 7842 are 1, 2, 3, 6, 1307, 2614, 3921, and 7842. Since none of these factors are perfect squares, the square root of 7842 cannot be simplified.

2) To be able to simplify the square root of 7842, all the prime factors of 7842 cannot be unique. When we did prime factorization of 7842, we found that 2 x 3 x 1307 equals 7842. Since all the prime factors are unique, the square root of 7842 cannot be simplified.

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