 # To check: Whether the set of numbers {sqrt{3}, pi, frac{sqrt{2}}{4}, sqrt{5}} contains integers, rational numbers, and (or) irrational numbers. Lewis Harvey 2020-10-18 Answered

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

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Result used: Rational number: Rational numbers are numbers that can be written in the form $\frac{p}{q}$, where p and q are integers with $q\ne 0$. 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 $\left\{\sqrt{3},\pi ,\frac{\sqrt{2}}{4},\sqrt{5}\right\}$ Observe that the elements 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 $\left\{\sqrt{3},\pi ,\frac{\sqrt{2}}{4},\sqrt{5}\right\}$ contains irrational numbers.