Simplify Square Root of 20306

What is the square root of 20306 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.

√20306 = A√B

Unfortunately, the square root of 20306 cannot be simplified. Thus, here is the answer to the square root of 20306 in its simplest form:

√ 20306 = √ 20306

Here are two different methods we used to determine why the square root of 20306 cannot be simplified.

1) To be able to simplify the square root of 20306, one of the factors of 20306 other than 1 must be a perfect square. The factors of 20306 are 1, 2, 11, 13, 22, 26, 71, 142, 143, 286, 781, 923, 1562, 1846, 10153, and 20306. Since none of these factors are perfect squares, the square root of 20306 cannot be simplified.

2) To be able to simplify the square root of 20306, all the prime factors of 20306 cannot be unique. When we did prime factorization of 20306, we found that 2 x 11 x 13 x 71 equals 20306. Since all the prime factors are unique, the square root of 20306 cannot be simplified.

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