Simplify Square Root of 4809




What is the square root of 4809 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.

4809 = A√B

Unfortunately, the square root of 4809 cannot be simplified. Thus, here is the answer to the square root of 4809 in its simplest form:

4809 = √ 4809


Here are two different methods we used to determine why the square root of 4809 cannot be simplified.

1) To be able to simplify the square root of 4809, one of the factors of 4809 other than 1 must be a perfect square. The factors of 4809 are 1, 3, 7, 21, 229, 687, 1603, and 4809. Since none of these factors are perfect squares, the square root of 4809 cannot be simplified.

2) To be able to simplify the square root of 4809, all the prime factors of 4809 cannot be unique. When we did prime factorization of 4809, we found that 3 x 7 x 229 equals 4809. Since all the prime factors are unique, the square root of 4809 cannot be simplified.



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