Simplify Square Root of 14385

What is the square root of 14385 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.

√14385 = A√B

Unfortunately, the square root of 14385 cannot be simplified. Thus, here is the answer to the square root of 14385 in its simplest form:

√ 14385 = √ 14385

Here are two different methods we used to determine why the square root of 14385 cannot be simplified.

1) To be able to simplify the square root of 14385, one of the factors of 14385 other than 1 must be a perfect square. The factors of 14385 are 1, 3, 5, 7, 15, 21, 35, 105, 137, 411, 685, 959, 2055, 2877, 4795, and 14385. Since none of these factors are perfect squares, the square root of 14385 cannot be simplified.

2) To be able to simplify the square root of 14385, all the prime factors of 14385 cannot be unique. When we did prime factorization of 14385, we found that 3 x 5 x 7 x 137 equals 14385. Since all the prime factors are unique, the square root of 14385 cannot be simplified.

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