Simplify Square Root of 7878

What is the square root of 7878 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.

√7878 = A√B

Unfortunately, the square root of 7878 cannot be simplified. Thus, here is the answer to the square root of 7878 in its simplest form:

√ 7878 = √ 7878

Here are two different methods we used to determine why the square root of 7878 cannot be simplified.

1) To be able to simplify the square root of 7878, one of the factors of 7878 other than 1 must be a perfect square. The factors of 7878 are 1, 2, 3, 6, 13, 26, 39, 78, 101, 202, 303, 606, 1313, 2626, 3939, and 7878. Since none of these factors are perfect squares, the square root of 7878 cannot be simplified.

2) To be able to simplify the square root of 7878, all the prime factors of 7878 cannot be unique. When we did prime factorization of 7878, we found that 2 x 3 x 13 x 101 equals 7878. Since all the prime factors are unique, the square root of 7878 cannot be simplified.

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