A rational number is a repeating decimal fraction, a fraction, or a decimal number you can write completely. Here, you might wonder about √1.69, but a quick check with your calculator shows that to be 1.3, a rational number.
In this list, the rationals are ...
22.74, -8, 0.25, 2/11, √1.69
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We assume that the "..." on the last two entries indicate each number goes on forever. The first one, 4.07... has a non-repeating pattern. The second one, 3.14... also has no repeating pattern, so both are irrational. 89 is not a perfect square, so its root will be irrational.