Rational and irrational numbers Knowledge-Based Download PDF

Questions

1. 1.

   Between which two consecutive integers does the irrational number $\sqrt{78}$ lie?

   • A) 8 and 9
   • B) 7 and 8
   • C) 9 and 10
   • D) 6 and 7
2. 2.

   Which of the following fractions represents the rational number $0.\overline{54}$ in simplest form?

   • A) $\frac{27}{50}$
   • B) $\frac{49}{90}$
   • C) $\frac{6}{11}$
   • D) $\frac{5}{9}$
3. 3.

   Which of the following statements about rational and irrational numbers is always true?

   • A) The product of two irrational numbers is always irrational.
   • B) The sum of two irrational numbers is always irrational.
   • C) The sum of a rational number and an irrational number is always irrational.
   • D) The product of a rational number and an irrational number is always irrational.
4. 4.

   Which of the following expressions simplifies to a rational number?

   • A) $\sqrt{12} + \sqrt{3}$
   • B) $\sqrt{8} \times \sqrt{3}$
   • C) $(\sqrt{7} - \sqrt{3})(\sqrt{7} + \sqrt{3})$
   • D) $\frac{\sqrt{50}}{3}$
5. 5.

   Which of the following numbers is an irrational number?

   • A) $\sqrt{0.49}$
   • B) $\sqrt{45}$
   • C) $3.\overline{14}$
   • D) $-\sqrt{\frac{64}{25}}$