Simplify Square Root of 30865

What is the square root of 30865 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.

√30865 = A√B

Unfortunately, the square root of 30865 cannot be simplified. Thus, here is the answer to the square root of 30865 in its simplest form:

√ 30865 = √ 30865

Here are two different methods we used to determine why the square root of 30865 cannot be simplified.

1) To be able to simplify the square root of 30865, one of the factors of 30865 other than 1 must be a perfect square. The factors of 30865 are 1, 5, 6173, and 30865. Since none of these factors are perfect squares, the square root of 30865 cannot be simplified.

2) To be able to simplify the square root of 30865, all the prime factors of 30865 cannot be unique. When we did prime factorization of 30865, we found that 5 x 6173 equals 30865. Since all the prime factors are unique, the square root of 30865 cannot be simplified.

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