Simplify Square Root of 80419

What is the square root of 80419 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.

√80419 = A√B

Unfortunately, the square root of 80419 cannot be simplified. Thus, here is the answer to the square root of 80419 in its simplest form:

√ 80419 = √ 80419

Here are two different methods we used to determine why the square root of 80419 cannot be simplified.

1) To be able to simplify the square root of 80419, one of the factors of 80419 other than 1 must be a perfect square. The factors of 80419 are 1, 137, 587, and 80419. Since none of these factors are perfect squares, the square root of 80419 cannot be simplified.

2) To be able to simplify the square root of 80419, all the prime factors of 80419 cannot be unique. When we did prime factorization of 80419, we found that 137 x 587 equals 80419. Since all the prime factors are unique, the square root of 80419 cannot be simplified.

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