Simplify Square Root of 19605

What is the square root of 19605 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.

√19605 = A√B

Unfortunately, the square root of 19605 cannot be simplified. Thus, here is the answer to the square root of 19605 in its simplest form:

√ 19605 = √ 19605

Here are two different methods we used to determine why the square root of 19605 cannot be simplified.

1) To be able to simplify the square root of 19605, one of the factors of 19605 other than 1 must be a perfect square. The factors of 19605 are 1, 3, 5, 15, 1307, 3921, 6535, and 19605. Since none of these factors are perfect squares, the square root of 19605 cannot be simplified.

2) To be able to simplify the square root of 19605, all the prime factors of 19605 cannot be unique. When we did prime factorization of 19605, we found that 3 x 5 x 1307 equals 19605. Since all the prime factors are unique, the square root of 19605 cannot be simplified.

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