Simplify Square Root of 1394

What is the square root of 1394 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.

√1394 = A√B

Unfortunately, the square root of 1394 cannot be simplified. Thus, here is the answer to the square root of 1394 in its simplest form:

√ 1394 = √ 1394

Here are two different methods we used to determine why the square root of 1394 cannot be simplified.

1) To be able to simplify the square root of 1394, one of the factors of 1394 other than 1 must be a perfect square. The factors of 1394 are 1, 2, 17, 34, 41, 82, 697, and 1394. Since none of these factors are perfect squares, the square root of 1394 cannot be simplified.

2) To be able to simplify the square root of 1394, all the prime factors of 1394 cannot be unique. When we did prime factorization of 1394, we found that 2 x 17 x 41 equals 1394. Since all the prime factors are unique, the square root of 1394 cannot be simplified.

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