Simplify Square Root of 12345

What is the square root of 12345 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.

√12345 = A√B

Unfortunately, the square root of 12345 cannot be simplified. Thus, here is the answer to the square root of 12345 in its simplest form:

√ 12345 = √ 12345

Here are two different methods we used to determine why the square root of 12345 cannot be simplified.

1) To be able to simplify the square root of 12345, one of the factors of 12345 other than 1 must be a perfect square. The factors of 12345 are 1, 3, 5, 15, 823, 2469, 4115, and 12345. Since none of these factors are perfect squares, the square root of 12345 cannot be simplified.

2) To be able to simplify the square root of 12345, all the prime factors of 12345 cannot be unique. When we did prime factorization of 12345, we found that 3 x 5 x 823 equals 12345. Since all the prime factors are unique, the square root of 12345 cannot be simplified.

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