← Back to topic
Vidaara.orgClass 9 · Mathematics
CodeVID-M09-01-IRR-01
Irrational Numbers & Representation — Assignment
Chapter: Number System
Topic: Irrational Numbers and Their Representation
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
$\sqrt2$ is:
  • A.rational
  • B.irrational
  • C.an integer
  • D.zero
2.
An irrational number's decimal is:
  • A.terminating
  • B.recurring
  • C.non-terminating non-recurring
  • D.finite
3.
$\sqrt{\text{(perfect square)}}$ is:
  • A.irrational
  • B.rational
  • C.not real
  • D.negative
4.
To represent $\sqrt2$ we use the:
  • A.distance formula
  • B.Pythagoras theorem
  • C.section formula
  • D.protractor
5.
$\pi$ is:
  • A.rational
  • B.irrational
  • C.terminating
  • D.an integer
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Is $\sqrt7$ rational or irrational?
7.
Is $\sqrt{25}$ irrational?
8.
Classify $2+\sqrt2$.
9.
To represent $\sqrt2$, what are the two legs of the right triangle?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Describe how to represent $\sqrt2$ on the number line.
11.
Describe how to represent $\sqrt3$ on the number line.
12.
Is $0.101001000100001\ldots$ rational or irrational?
13.
Give an irrational number between $2$ and $3$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Represent $\sqrt5$ on the number line using the Pythagorean construction.
15.
Find an irrational number between $\tfrac17$ and $\tfrac27$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) irrational
  2. (C) non-terminating non-recurring
  3. (B) rational
  4. (B) Pythagoras theorem
  5. (B) irrational
Section B — Short Answer (2 marks)
  1. Irrational.
  2. No ($=5$).
  3. Irrational.
  4. $1$ and $1$.
Section C — Short Answer (3 marks)
  1. Right triangle with legs $1,1$ gives hypotenuse $\sqrt2$; transfer it with a compass.
  2. On the $\sqrt2$ segment erect a perpendicular of length $1$; the new hypotenuse is $\sqrt3$.
  3. Irrational.
  4. e.g. $\sqrt5$.
Section D — Long Answer (5 marks)
  1. Right triangle with legs $2$ and $1$ gives hypotenuse $\sqrt5$; transfer with a compass.
  2. e.g. $0.150150015000\ldots$ (non-terminating, non-recurring).
Generated by Vidaara.org · Assignment VID-M09-01-IRR-01 · vidaara.org