Simplify Square Root of 19545

What is the square root of 19545 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.

√19545 = A√B

Unfortunately, the square root of 19545 cannot be simplified. Thus, here is the answer to the square root of 19545 in its simplest form:

√ 19545 = √ 19545

Here are two different methods we used to determine why the square root of 19545 cannot be simplified.

1) To be able to simplify the square root of 19545, one of the factors of 19545 other than 1 must be a perfect square. The factors of 19545 are 1, 3, 5, 15, 1303, 3909, 6515, and 19545. Since none of these factors are perfect squares, the square root of 19545 cannot be simplified.

2) To be able to simplify the square root of 19545, all the prime factors of 19545 cannot be unique. When we did prime factorization of 19545, we found that 3 x 5 x 1303 equals 19545. Since all the prime factors are unique, the square root of 19545 cannot be simplified.

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