Simplify Square Root of 1909

What is the square root of 1909 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.

√1909 = A√B

Unfortunately, the square root of 1909 cannot be simplified. Thus, here is the answer to the square root of 1909 in its simplest form:

√ 1909 = √ 1909

Here are two different methods we used to determine why the square root of 1909 cannot be simplified.

1) To be able to simplify the square root of 1909, one of the factors of 1909 other than 1 must be a perfect square. The factors of 1909 are 1, 23, 83, and 1909. Since none of these factors are perfect squares, the square root of 1909 cannot be simplified.

2) To be able to simplify the square root of 1909, all the prime factors of 1909 cannot be unique. When we did prime factorization of 1909, we found that 23 x 83 equals 1909. Since all the prime factors are unique, the square root of 1909 cannot be simplified.

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