Simplify Square Root of 13906

What is the square root of 13906 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.

√13906 = A√B

Unfortunately, the square root of 13906 cannot be simplified. Thus, here is the answer to the square root of 13906 in its simplest form:

√ 13906 = √ 13906

Here are two different methods we used to determine why the square root of 13906 cannot be simplified.

1) To be able to simplify the square root of 13906, one of the factors of 13906 other than 1 must be a perfect square. The factors of 13906 are 1, 2, 17, 34, 409, 818, 6953, and 13906. Since none of these factors are perfect squares, the square root of 13906 cannot be simplified.

2) To be able to simplify the square root of 13906, all the prime factors of 13906 cannot be unique. When we did prime factorization of 13906, we found that 2 x 17 x 409 equals 13906. Since all the prime factors are unique, the square root of 13906 cannot be simplified.

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