Simplify Square Root of 78513

What is the square root of 78513 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.

√78513 = A√B

Unfortunately, the square root of 78513 cannot be simplified. Thus, here is the answer to the square root of 78513 in its simplest form:

√ 78513 = √ 78513

Here are two different methods we used to determine why the square root of 78513 cannot be simplified.

1) To be able to simplify the square root of 78513, one of the factors of 78513 other than 1 must be a perfect square. The factors of 78513 are 1, 3, 26171, and 78513. Since none of these factors are perfect squares, the square root of 78513 cannot be simplified.

2) To be able to simplify the square root of 78513, all the prime factors of 78513 cannot be unique. When we did prime factorization of 78513, we found that 3 x 26171 equals 78513. Since all the prime factors are unique, the square root of 78513 cannot be simplified.

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