Simplify Square Root of 28633

What is the square root of 28633 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.

√28633 = A√B

Unfortunately, the square root of 28633 cannot be simplified. Thus, here is the answer to the square root of 28633 in its simplest form:

√ 28633 = √ 28633

Here are two different methods we used to determine why the square root of 28633 cannot be simplified.

1) To be able to simplify the square root of 28633, one of the factors of 28633 other than 1 must be a perfect square. The factors of 28633 are 1, 11, 19, 137, 209, 1507, 2603, and 28633. Since none of these factors are perfect squares, the square root of 28633 cannot be simplified.

2) To be able to simplify the square root of 28633, all the prime factors of 28633 cannot be unique. When we did prime factorization of 28633, we found that 11 x 19 x 137 equals 28633. Since all the prime factors are unique, the square root of 28633 cannot be simplified.

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