← Back to topic
Vidaara.orgClass 8 · Mathematics
CodeVID-M08-02-IRR-01
What Are Irrational Numbers - Assignment
Chapter: Irrational Numbers
Topic: What Are Irrational Numbers?
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.
An irrational number cannot be written as:
  • A.a decimal
  • B.$\tfrac{p}{q}$
  • C.a surd
  • D.a root
2.
The decimal form of an irrational number is:
  • A.terminating
  • B.repeating
  • C.non-terminating, non-repeating
  • D.zero
3.
Which is irrational?
  • A.$\sqrt9$
  • B.$\sqrt2$
  • C.$\tfrac{22}{7}$
  • D.$0.5$
4.
$\pi$ is:
  • A.rational
  • B.irrational
  • C.an integer
  • D.a fraction
5.
$\sqrt9$ is:
  • A.irrational
  • B.rational
  • C.not a number
  • D.negative
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Is $\sqrt3$ rational or irrational?
7.
Is $\sqrt{16}$ rational or irrational?
8.
Give one example of an irrational number.
9.
Is $0.1010010001\ldots$ rational?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Classify as rational/irrational: $\sqrt5,\ \sqrt{25},\ \tfrac{22}{7},\ \pi$.
11.
Is $0.\overline{3}$ rational? Why?
12.
Between which two integers does $\sqrt7$ lie?
13.
Is $\sqrt2\times\sqrt2$ rational?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Classify each as rational or irrational and justify: $\sqrt{36},\ \sqrt8,\ 3.14,\ 0.121221222\ldots$
15.
State whether $\sqrt2+3$ is irrational and find two integers it lies between.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\tfrac{p}{q}$
  2. (C) non-terminating, non-repeating
  3. (B) $\sqrt2$
  4. (B) irrational
  5. (B) rational
Section B — Short Answer (2 marks)
  1. Irrational.
  2. Rational ($=4$).
  3. $\sqrt2$ (or $\pi$).
  4. No, it is irrational (non-repeating).
Section C — Short Answer (3 marks)
  1. Irrational, rational, rational, irrational.
  2. Yes — it is a repeating decimal.
  3. $2$ and $3$.
  4. Yes ($=2$).
Section D — Long Answer (5 marks)
  1. $\sqrt{36}=6$ rational; $\sqrt8$ irrational; $3.14$ rational (terminating); $0.121221222\ldots$ irrational (non-repeating).
  2. Irrational; it lies between $4$ and $5$.
Generated by Vidaara.org · Assignment VID-M08-02-IRR-01 · vidaara.org