Simplify Square Root of 77118

What is the square root of 77118 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.

√77118 = A√B

Unfortunately, the square root of 77118 cannot be simplified. Thus, here is the answer to the square root of 77118 in its simplest form:

√ 77118 = √ 77118

Here are two different methods we used to determine why the square root of 77118 cannot be simplified.

1) To be able to simplify the square root of 77118, one of the factors of 77118 other than 1 must be a perfect square. The factors of 77118 are 1, 2, 3, 6, 12853, 25706, 38559, and 77118. Since none of these factors are perfect squares, the square root of 77118 cannot be simplified.

2) To be able to simplify the square root of 77118, all the prime factors of 77118 cannot be unique. When we did prime factorization of 77118, we found that 2 x 3 x 12853 equals 77118. Since all the prime factors are unique, the square root of 77118 cannot be simplified.

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