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Vidaara.orgClass 8 · Mathematics
CodeVID-M8-02-CT
Irrational Numbers — Full Chapter Test
Chapter: Irrational Numbers
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • 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.
$\sqrt a\times\sqrt b=$
  • A.$\sqrt{a+b}$
  • B.$\sqrt{ab}$
  • C.$ab$
  • D.$\sqrt a+\sqrt b$
3.
Real numbers consist of:
  • A.only integers
  • B.rationals and irrationals
  • C.only fractions
  • D.only surds
4.
The decimal form of an irrational number is:
  • A.terminating
  • B.repeating
  • C.non-terminating, non-repeating
  • D.zero
5.
$\sqrt8=$
  • A.$2\sqrt2$
  • B.$4\sqrt2$
  • C.$2\sqrt4$
  • D.$8$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Is $\sqrt3$ rational or irrational?
7.
Simplify $\sqrt{12}$.
8.
Is every rational number a real number?
9.
Is $\sqrt{16}$ rational or irrational?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Classify as rational/irrational: $\sqrt5,\ \sqrt{25},\ \tfrac{22}{7},\ \pi$.
11.
Simplify $\sqrt{18}+\sqrt2$.
12.
Between which integers does $\sqrt{10}$ lie?
13.
Is $0.\overline{3}$ rational? Why?
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.
Simplify $2\sqrt{27}+\sqrt{48}-\sqrt{12}$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\tfrac{p}{q}$
  2. (B) $\sqrt{ab}$
  3. (B) rationals and irrationals
  4. (C) non-terminating, non-repeating
  5. (A) $2\sqrt2$
Section B — Short Answer (2 marks)
  1. Irrational.
  2. $2\sqrt3$.
  3. Yes.
  4. Rational ($=4$).
Section C — Short Answer (3 marks)
  1. Irrational, rational, rational, irrational.
  2. $4\sqrt2$.
  3. $3$ and $4$.
  4. Yes — it is a repeating decimal.
Section D — Long Answer (5 marks)
  1. $\sqrt{36}=6$ rational; $\sqrt8$ irrational; $3.14$ rational (terminating); $0.121221222\ldots$ irrational (non-repeating).
  2. $8\sqrt3$.
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