Vidaara.orgClass 9 · Mathematics
CodeVID-M09-01-OPR-01
Operations on Real 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.
Rational $+$ irrational $=$
- A.rational
- B.irrational
- C.zero
- D.integer
2.
A non-zero rational $\times$ irrational $=$
- A.rational
- B.irrational
- C.zero
- D.integer
3.
The real numbers are closed under:
- A.addition and multiplication
- B.neither
- C.division by zero
- D.only addition
4.
$\sqrt2\times\sqrt2=$
- A.$\sqrt2$
- B.$2$
- C.$4$
- D.$2\sqrt2$
5.
The sum of two irrationals may be:
- A.only irrational
- B.rational or irrational
- C.only rational
- D.zero only
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Is $2+\sqrt3$ rational or irrational?
7.
Find $\sqrt3\times\sqrt{12}$.
8.
Simplify $\sqrt{50}$.
9.
Is $(\sqrt2)(\sqrt2)$ rational?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Simplify $\sqrt8+\sqrt{18}$.
11.
Simplify $(3+\sqrt5)(3-\sqrt5)$.
12.
Simplify $\sqrt{45}-\sqrt{20}$.
13.
Give two irrationals whose sum is rational.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Simplify $(5+\sqrt3)(5-\sqrt3)+(\sqrt7)^2$.
15.
Simplify $(\sqrt5+\sqrt2)^2$ and state whether it is rational or irrational.
Answer Key
Section A — Multiple Choice Questions
- (B) irrational
- (B) irrational
- (A) addition and multiplication
- (B) $2$
- (B) rational or irrational
Section B — Short Answer (2 marks)
- Irrational.
- $6$.
- $5\sqrt2$.
- Yes ($=2$).
Section C — Short Answer (3 marks)
- $5\sqrt2$.
- $4$.
- $\sqrt5$.
- $\sqrt2$ and $-\sqrt2$.
Section D — Long Answer (5 marks)
- $29$.
- $7+2\sqrt{10}$ (irrational).
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