Simplify Square Root of 8530

What is the square root of 8530 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.

√8530 = A√B

Unfortunately, the square root of 8530 cannot be simplified. Thus, here is the answer to the square root of 8530 in its simplest form:

√ 8530 = √ 8530

Here are two different methods we used to determine why the square root of 8530 cannot be simplified.

1) To be able to simplify the square root of 8530, one of the factors of 8530 other than 1 must be a perfect square. The factors of 8530 are 1, 2, 5, 10, 853, 1706, 4265, and 8530. Since none of these factors are perfect squares, the square root of 8530 cannot be simplified.

2) To be able to simplify the square root of 8530, all the prime factors of 8530 cannot be unique. When we did prime factorization of 8530, we found that 2 x 5 x 853 equals 8530. Since all the prime factors are unique, the square root of 8530 cannot be simplified.

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