Simplify Square Root of 19005

What is the square root of 19005 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.

√19005 = A√B

Unfortunately, the square root of 19005 cannot be simplified. Thus, here is the answer to the square root of 19005 in its simplest form:

√ 19005 = √ 19005

Here are two different methods we used to determine why the square root of 19005 cannot be simplified.

1) To be able to simplify the square root of 19005, one of the factors of 19005 other than 1 must be a perfect square. The factors of 19005 are 1, 3, 5, 7, 15, 21, 35, 105, 181, 543, 905, 1267, 2715, 3801, 6335, and 19005. Since none of these factors are perfect squares, the square root of 19005 cannot be simplified.

2) To be able to simplify the square root of 19005, all the prime factors of 19005 cannot be unique. When we did prime factorization of 19005, we found that 3 x 5 x 7 x 181 equals 19005. Since all the prime factors are unique, the square root of 19005 cannot be simplified.

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