Simplify Square Root of 30561

What is the square root of 30561 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.

√30561 = A√B

Unfortunately, the square root of 30561 cannot be simplified. Thus, here is the answer to the square root of 30561 in its simplest form:

√ 30561 = √ 30561

Here are two different methods we used to determine why the square root of 30561 cannot be simplified.

1) To be able to simplify the square root of 30561, one of the factors of 30561 other than 1 must be a perfect square. The factors of 30561 are 1, 3, 61, 167, 183, 501, 10187, and 30561. Since none of these factors are perfect squares, the square root of 30561 cannot be simplified.

2) To be able to simplify the square root of 30561, all the prime factors of 30561 cannot be unique. When we did prime factorization of 30561, we found that 3 x 61 x 167 equals 30561. Since all the prime factors are unique, the square root of 30561 cannot be simplified.

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