Simplify Square Root of 11742

What is the square root of 11742 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.

√11742 = A√B

Unfortunately, the square root of 11742 cannot be simplified. Thus, here is the answer to the square root of 11742 in its simplest form:

√ 11742 = √ 11742

Here are two different methods we used to determine why the square root of 11742 cannot be simplified.

1) To be able to simplify the square root of 11742, one of the factors of 11742 other than 1 must be a perfect square. The factors of 11742 are 1, 2, 3, 6, 19, 38, 57, 103, 114, 206, 309, 618, 1957, 3914, 5871, and 11742. Since none of these factors are perfect squares, the square root of 11742 cannot be simplified.

2) To be able to simplify the square root of 11742, all the prime factors of 11742 cannot be unique. When we did prime factorization of 11742, we found that 2 x 3 x 19 x 103 equals 11742. Since all the prime factors are unique, the square root of 11742 cannot be simplified.

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