Simplify Square Root of 19495

What is the square root of 19495 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.

√19495 = A√B

Unfortunately, the square root of 19495 cannot be simplified. Thus, here is the answer to the square root of 19495 in its simplest form:

√ 19495 = √ 19495

Here are two different methods we used to determine why the square root of 19495 cannot be simplified.

1) To be able to simplify the square root of 19495, one of the factors of 19495 other than 1 must be a perfect square. The factors of 19495 are 1, 5, 7, 35, 557, 2785, 3899, and 19495. Since none of these factors are perfect squares, the square root of 19495 cannot be simplified.

2) To be able to simplify the square root of 19495, all the prime factors of 19495 cannot be unique. When we did prime factorization of 19495, we found that 5 x 7 x 557 equals 19495. Since all the prime factors are unique, the square root of 19495 cannot be simplified.

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