Simplify Square Root of 74819

What is the square root of 74819 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.

√74819 = A√B

Unfortunately, the square root of 74819 cannot be simplified. Thus, here is the answer to the square root of 74819 in its simplest form:

√ 74819 = √ 74819

Here are two different methods we used to determine why the square root of 74819 cannot be simplified.

1) To be able to simplify the square root of 74819, one of the factors of 74819 other than 1 must be a perfect square. The factors of 74819 are 1, 23, 3253, and 74819. Since none of these factors are perfect squares, the square root of 74819 cannot be simplified.

2) To be able to simplify the square root of 74819, all the prime factors of 74819 cannot be unique. When we did prime factorization of 74819, we found that 23 x 3253 equals 74819. Since all the prime factors are unique, the square root of 74819 cannot be simplified.

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