Rational and irrational numbers Knowledge-Based Practice

Questions

1. 1.

   Which of the following statements is always true?

   • A) The product of two irrational numbers is always an irrational number.
   • B) The sum of two irrational numbers is always an irrational number.
   • C) The quotient of two non-zero irrational numbers is always an irrational number.
   • D) The difference of two rational numbers is always a rational number.
2. 2.

   Let $r$ be a non-zero rational number and $s$ be an irrational number. Which of the following expressions must always result in an irrational number?

   • A) $s^2$
   • B) $r \cdot s$
   • C) $s + \sqrt{5}$
   • D) $\frac{s}{s}$
3. 3.

   Which of the following statements correctly characterizes the decimal expansion of any irrational number?

   • A) It terminates after a finite number of digits.
   • B) It is non-terminating and does not repeat periodically.
   • C) It eventually settles into an infinitely repeating sequence of digits.
   • D) It can always be written as a ratio of two integers with a non-zero denominator.
4. 4.

   Which of the following expressions evaluates to a rational number?

   • A) $\sqrt{8} + \sqrt{2}$
   • B) $(\sqrt{7} - 2)(\sqrt{7} + 2)$
   • C) $\sqrt{3} \times \sqrt{5}$
   • D) $\frac{\sqrt{18}}{3}$
5. 5.

   Which of the following numbers is an irrational number?

   • A) $\sqrt{144}$
   • B) $0.\overline{45}$
   • C) $\sqrt{18}$
   • D) $-\frac{17}{8}$

Answers and step-by-step solutions appear after you finish the test.