To check: Whether the set of numbers {3,π,234,5} contains integers, rational numbers, and (or) irrational numbers.

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Sally Cresswell · Accepted Answer

Result used: Rational number: Rational numbers are numbers that can be written in the form pq, where p and q are integers with q≠0. The rational numbers can be written as terminating or repeating decimals. Irrational number: The irrational numbers are set of all real numbers that not rational numbers. The irrationals cannot be written as terminating or repeating decimals. Verification: The given set of numbers is {3,π,234,5} Observe that the elements 3=1.732 ... ,π=3.14 ... ,234=0.315 ... ,and 5=2.236 ... are non-terminating decimals. Therefore, by the definition of the irrational numbers, all the numbers in the given set are irrational. Answer: Thus, the set numbers {3,π,234,5} contains irrational numbers.

To check: Whether the set of numbers {sqrt{3}, pi, frac{sqrt[3]{2}}{4}, sqrt{5}} contains integers, rational numbers, and (or) irrational numbers.

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