Simplify Square Root of 20809

What is the square root of 20809 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.

√20809 = A√B

Unfortunately, the square root of 20809 cannot be simplified. Thus, here is the answer to the square root of 20809 in its simplest form:

√ 20809 = √ 20809

Here are two different methods we used to determine why the square root of 20809 cannot be simplified.

1) To be able to simplify the square root of 20809, one of the factors of 20809 other than 1 must be a perfect square. The factors of 20809 are 1 and 20809. Since none of these factors are perfect squares, the square root of 20809 cannot be simplified.

2) To be able to simplify the square root of 20809, all the prime factors of 20809 cannot be unique. When we did prime factorization of 20809, we found that 20809 equals 20809. Since all the prime factors are unique, the square root of 20809 cannot be simplified.

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