Simplify Square Root of 12390

What is the square root of 12390 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.

√12390 = A√B

Unfortunately, the square root of 12390 cannot be simplified. Thus, here is the answer to the square root of 12390 in its simplest form:

√ 12390 = √ 12390

Here are two different methods we used to determine why the square root of 12390 cannot be simplified.

1) To be able to simplify the square root of 12390, one of the factors of 12390 other than 1 must be a perfect square. The factors of 12390 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 59, 70, 105, 118, 177, 210, 295, 354, 413, 590, 826, 885, 1239, 1770, 2065, 2478, 4130, 6195, and 12390. Since none of these factors are perfect squares, the square root of 12390 cannot be simplified.

2) To be able to simplify the square root of 12390, all the prime factors of 12390 cannot be unique. When we did prime factorization of 12390, we found that 2 x 3 x 5 x 7 x 59 equals 12390. Since all the prime factors are unique, the square root of 12390 cannot be simplified.

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