Simplify Square Root of 47730

What is the square root of 47730 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.

√47730 = A√B

Unfortunately, the square root of 47730 cannot be simplified. Thus, here is the answer to the square root of 47730 in its simplest form:

√ 47730 = √ 47730

Here are two different methods we used to determine why the square root of 47730 cannot be simplified.

1) To be able to simplify the square root of 47730, one of the factors of 47730 other than 1 must be a perfect square. The factors of 47730 are 1, 2, 3, 5, 6, 10, 15, 30, 37, 43, 74, 86, 111, 129, 185, 215, 222, 258, 370, 430, 555, 645, 1110, 1290, 1591, 3182, 4773, 7955, 9546, 15910, 23865, and 47730. Since none of these factors are perfect squares, the square root of 47730 cannot be simplified.

2) To be able to simplify the square root of 47730, all the prime factors of 47730 cannot be unique. When we did prime factorization of 47730, we found that 2 x 3 x 5 x 37 x 43 equals 47730. Since all the prime factors are unique, the square root of 47730 cannot be simplified.

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