Simplify Square Root of 24414

What is the square root of 24414 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.

√24414 = A√B

Unfortunately, the square root of 24414 cannot be simplified. Thus, here is the answer to the square root of 24414 in its simplest form:

√ 24414 = √ 24414

Here are two different methods we used to determine why the square root of 24414 cannot be simplified.

1) To be able to simplify the square root of 24414, one of the factors of 24414 other than 1 must be a perfect square. The factors of 24414 are 1, 2, 3, 6, 13, 26, 39, 78, 313, 626, 939, 1878, 4069, 8138, 12207, and 24414. Since none of these factors are perfect squares, the square root of 24414 cannot be simplified.

2) To be able to simplify the square root of 24414, all the prime factors of 24414 cannot be unique. When we did prime factorization of 24414, we found that 2 x 3 x 13 x 313 equals 24414. Since all the prime factors are unique, the square root of 24414 cannot be simplified.

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