Simplify Square Root of 78474

What is the square root of 78474 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.

√78474 = A√B

Unfortunately, the square root of 78474 cannot be simplified. Thus, here is the answer to the square root of 78474 in its simplest form:

√ 78474 = √ 78474

Here are two different methods we used to determine why the square root of 78474 cannot be simplified.

1) To be able to simplify the square root of 78474, one of the factors of 78474 other than 1 must be a perfect square. The factors of 78474 are 1, 2, 3, 6, 11, 22, 29, 33, 41, 58, 66, 82, 87, 123, 174, 246, 319, 451, 638, 902, 957, 1189, 1353, 1914, 2378, 2706, 3567, 7134, 13079, 26158, 39237, and 78474. Since none of these factors are perfect squares, the square root of 78474 cannot be simplified.

2) To be able to simplify the square root of 78474, all the prime factors of 78474 cannot be unique. When we did prime factorization of 78474, we found that 2 x 3 x 11 x 29 x 41 equals 78474. Since all the prime factors are unique, the square root of 78474 cannot be simplified.

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