Question

Which of the following is an example of a rational number?

Answer 1

Answer: Choice B

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Explanation:

Using your calculator, you should find that

• sqrt(125) = 11.1803 approximately
• sqrt(196) = 14 exactly
• sqrt(207) = 14.387 approximately
• sqrt(220) = 14.832 approximately

Each approximate result has its decimal digits go on forever without any pattern. So we cannot write those values as a fraction of two integers. The decimal expansion must have some kind of pattern that repeats forever, so we could consider it rational.

Only choice B results in a whole number. The value 14 is the same as 14/1, showing it can be written as a fraction of two integers. Therefore choice B is rational.