Simplify Square Root of 19985

What is the square root of 19985 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.

√19985 = A√B

Unfortunately, the square root of 19985 cannot be simplified. Thus, here is the answer to the square root of 19985 in its simplest form:

√ 19985 = √ 19985

Here are two different methods we used to determine why the square root of 19985 cannot be simplified.

1) To be able to simplify the square root of 19985, one of the factors of 19985 other than 1 must be a perfect square. The factors of 19985 are 1, 5, 7, 35, 571, 2855, 3997, and 19985. Since none of these factors are perfect squares, the square root of 19985 cannot be simplified.

2) To be able to simplify the square root of 19985, all the prime factors of 19985 cannot be unique. When we did prime factorization of 19985, we found that 5 x 7 x 571 equals 19985. Since all the prime factors are unique, the square root of 19985 cannot be simplified.

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