Vidaara.orgClass 10 · Mathematics
CodeVID-M10-01-IRR-01
Revisiting Irrational Numbers — Assignment
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.
The product of a non-zero rational and an irrational is:
- A.rational
- B.irrational
- C.zero
- D.an integer
3.
$\sqrt9$ is:
- A.irrational
- B.rational
- C.not real
- D.negative
4.
$\pi$ is:
- A.rational
- B.irrational
- C.terminating
- D.an integer
5.
A non-terminating non-repeating decimal is:
- A.rational
- B.irrational
- C.an integer
- D.terminating
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Is $3+\sqrt2$ rational or irrational?
7.
Is $\sqrt{16}$ rational?
8.
Classify $2\sqrt3$.
9.
Is $0.\overline{3}$ rational?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Prove that $\sqrt2$ is irrational (state the method).
11.
Show that $5-\sqrt3$ is irrational.
12.
Show that $3\sqrt2$ is irrational.
13.
Is $\sqrt2+\sqrt3$ rational or irrational?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Prove that $\sqrt5$ is irrational.
15.
Prove that $3+2\sqrt5$ is irrational, given that $\sqrt5$ is irrational.
Answer Key
Section A — Multiple Choice Questions
- (B) irrational
- (B) irrational
- (B) rational
- (B) irrational
- (B) irrational
Section B — Short Answer (2 marks)
- Irrational.
- Yes ($=4$).
- Irrational.
- Yes ($=\tfrac13$).
Section C — Short Answer (3 marks)
- By contradiction; $\sqrt2$ is irrational.
- Irrational.
- Irrational.
- Irrational.
Section D — Long Answer (5 marks)
- By contradiction, $\sqrt5$ is irrational.
- Irrational.
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