Simplify Square Root of 24789

What is the square root of 24789 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.

√24789 = A√B

Unfortunately, the square root of 24789 cannot be simplified. Thus, here is the answer to the square root of 24789 in its simplest form:

√ 24789 = √ 24789

Here are two different methods we used to determine why the square root of 24789 cannot be simplified.

1) To be able to simplify the square root of 24789, one of the factors of 24789 other than 1 must be a perfect square. The factors of 24789 are 1, 3, 8263, and 24789. Since none of these factors are perfect squares, the square root of 24789 cannot be simplified.

2) To be able to simplify the square root of 24789, all the prime factors of 24789 cannot be unique. When we did prime factorization of 24789, we found that 3 x 8263 equals 24789. Since all the prime factors are unique, the square root of 24789 cannot be simplified.

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