Simplify Square Root of 30543

What is the square root of 30543 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.

√30543 = A√B

Unfortunately, the square root of 30543 cannot be simplified. Thus, here is the answer to the square root of 30543 in its simplest form:

√ 30543 = √ 30543

Here are two different methods we used to determine why the square root of 30543 cannot be simplified.

1) To be able to simplify the square root of 30543, one of the factors of 30543 other than 1 must be a perfect square. The factors of 30543 are 1, 3, 10181, and 30543. Since none of these factors are perfect squares, the square root of 30543 cannot be simplified.

2) To be able to simplify the square root of 30543, all the prime factors of 30543 cannot be unique. When we did prime factorization of 30543, we found that 3 x 10181 equals 30543. Since all the prime factors are unique, the square root of 30543 cannot be simplified.

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