Simplify Square Root of 19142

What is the square root of 19142 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.

√19142 = A√B

Unfortunately, the square root of 19142 cannot be simplified. Thus, here is the answer to the square root of 19142 in its simplest form:

√ 19142 = √ 19142

Here are two different methods we used to determine why the square root of 19142 cannot be simplified.

1) To be able to simplify the square root of 19142, one of the factors of 19142 other than 1 must be a perfect square. The factors of 19142 are 1, 2, 17, 34, 563, 1126, 9571, and 19142. Since none of these factors are perfect squares, the square root of 19142 cannot be simplified.

2) To be able to simplify the square root of 19142, all the prime factors of 19142 cannot be unique. When we did prime factorization of 19142, we found that 2 x 17 x 563 equals 19142. Since all the prime factors are unique, the square root of 19142 cannot be simplified.

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