g
Gyaan Maths
CBSE · Class 6-10
Back to chapter
CBSE Maths · Class 9

Chapter 1: Number Systems

Name: ________________________
Date: ______________
Marks: ____ / 10

Rational and irrational numbers, decimal expansions, representation on the number line, and laws of exponents for real numbers.

Questions

  1. Is zero a rational number?
  2. Find three rationals between 3/53/5 and 4/54/5.
  3. Simplify 21/3⋅21/42^{1/3}\cdot 2^{1/4}.
  4. Prove 2\sqrt 2 is irrational.
  5. Express 0.3‾0.\overline{3} as p/qp/q.
  6. Rationalise 17−6\dfrac{1}{\sqrt 7 - \sqrt 6}.
  7. Rationalise 12+3\dfrac{1}{2 + \sqrt 3}.
  8. Evaluate (32/3)3/2(3^{2/3})^{3/2}.
  9. Simplify 45+320−45\sqrt{45} + 3\sqrt{20} - 4\sqrt{5}.
  10. Find two irrationals between 22 and 33.

Extra Practice (Optional)

  • Express 0.6‾0.\overline{6} as p/qp/q.
  • Rationalise 13+2\dfrac{1}{\sqrt 3 + \sqrt 2}.
  • Simplify (16)−1/4(16)^{-1/4}.
  • Show 5\sqrt 5 is irrational.
  • Locate 7.3\sqrt{7.3} on the number line.

Answer Key (For Teachers)

  1. Answer: Yes.
    Working: 0=0/10 = 0/1.
  2. Answer: 13/20,7/10,3/413/20, 7/10, 3/4.
    Working: Use denominator 2020.
  3. Answer: 27/122^{7/12}.
    Working: Add exponents: 7/127/12.
  4. Answer: Irrational.
    Working: Contradiction; parity argument.
  5. Answer: 1/31/3.
    Working: 10x−x=310x - x = 3.
  6. Answer: 7+6\sqrt 7 + \sqrt 6.
    Working: Multiply by conjugate.
  7. Answer: 2−32 - \sqrt 3.
    Working: Conjugate 2−32 - \sqrt 3.
  8. Answer: 33.
    Working: Product of exponents.
  9. Answer: 555\sqrt 5.
    Working: 45=35\sqrt{45} = 3\sqrt 5; 320=653\sqrt{20} = 6\sqrt 5; total =35+65−45=55= 3\sqrt 5 + 6\sqrt 5 - 4\sqrt 5 = 5\sqrt 5.
  10. Answer: 5,7\sqrt 5, \sqrt 7.
    Working: 5≈2.24\sqrt 5 \approx 2.24; 7≈2.65\sqrt 7 \approx 2.65.
Gyaan Maths · CBSE Class 9 · Chapter 1
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026