Simplify Square Root of 47830

What is the square root of 47830 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.

√47830 = A√B

Unfortunately, the square root of 47830 cannot be simplified. Thus, here is the answer to the square root of 47830 in its simplest form:

√ 47830 = √ 47830

Here are two different methods we used to determine why the square root of 47830 cannot be simplified.

1) To be able to simplify the square root of 47830, one of the factors of 47830 other than 1 must be a perfect square. The factors of 47830 are 1, 2, 5, 10, 4783, 9566, 23915, and 47830. Since none of these factors are perfect squares, the square root of 47830 cannot be simplified.

2) To be able to simplify the square root of 47830, all the prime factors of 47830 cannot be unique. When we did prime factorization of 47830, we found that 2 x 5 x 4783 equals 47830. Since all the prime factors are unique, the square root of 47830 cannot be simplified.

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