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0.123124125…. - This number is a rational number since it is a repeating decimal pattern.
√17 - This number is an irrational number since it cannot be expressed as a simple fraction and its decimal representation goes on forever without repeating.
√49 - This number is a rational number since it can be expressed as a whole number (7).
0.567 - This number is a rational number since it can be expressed as a simple fraction (567/1000) and its decimal representation terminates.
0.898989… - This number is a rational number since it is a repeating decimal pattern.