Simplify Square Root of 30506

What is the square root of 30506 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.

√30506 = A√B

Unfortunately, the square root of 30506 cannot be simplified. Thus, here is the answer to the square root of 30506 in its simplest form:

√ 30506 = √ 30506

Here are two different methods we used to determine why the square root of 30506 cannot be simplified.

1) To be able to simplify the square root of 30506, one of the factors of 30506 other than 1 must be a perfect square. The factors of 30506 are 1, 2, 7, 14, 2179, 4358, 15253, and 30506. Since none of these factors are perfect squares, the square root of 30506 cannot be simplified.

2) To be able to simplify the square root of 30506, all the prime factors of 30506 cannot be unique. When we did prime factorization of 30506, we found that 2 x 7 x 2179 equals 30506. Since all the prime factors are unique, the square root of 30506 cannot be simplified.

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