← Back to topic
Vidaara.orgClass 9 · Mathematics
CodeVID-M09-01-RAT-01
Rationalization — Assignment
Chapter: Number System
Topic: Rationalization of Real 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.
Rationalizing $\dfrac{1}{\sqrt2}$ gives:
  • A.$\tfrac{\sqrt2}{2}$
  • B.$\sqrt2$
  • C.$2$
  • D.$\tfrac12$
2.
The rationalizing factor of $\sqrt a$ is:
  • A.$a$
  • B.$\sqrt a$
  • C.$\tfrac1a$
  • D.$a^2$
3.
The conjugate of $(a+\sqrt b)$ is:
  • A.$(a+\sqrt b)$
  • B.$(a-\sqrt b)$
  • C.$(\sqrt b-a)$
  • D.$(b-a)$
4.
$\dfrac{1}{\sqrt3}$ rationalized is:
  • A.$\tfrac{\sqrt3}{3}$
  • B.$\sqrt3$
  • C.$3$
  • D.$\tfrac13$
5.
Rationalization removes the radical from the:
  • A.numerator
  • B.denominator
  • C.exponent
  • D.coefficient
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Rationalize $\dfrac{1}{\sqrt5}$.
7.
Rationalize $\dfrac{1}{\sqrt7}$.
8.
Write the conjugate of $2+\sqrt3$.
9.
Rationalize $\dfrac{3}{\sqrt2}$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Rationalize $\dfrac{1}{\sqrt3-\sqrt2}$.
11.
Rationalize $\dfrac{1}{2+\sqrt3}$.
12.
Rationalize $\dfrac{5}{\sqrt6+1}$.
13.
Simplify $\dfrac{1}{3+2\sqrt2}$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Rationalize and simplify $\dfrac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3}$.
15.
If $\dfrac{1}{\sqrt2-1}=a+b\sqrt2$, find $a$ and $b$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\tfrac{\sqrt2}{2}$
  2. (B) $\sqrt a$
  3. (B) $(a-\sqrt b)$
  4. (A) $\tfrac{\sqrt3}{3}$
  5. (B) denominator
Section B — Short Answer (2 marks)
  1. $\tfrac{\sqrt5}{5}$.
  2. $\tfrac{\sqrt7}{7}$.
  3. $2-\sqrt3$.
  4. $\tfrac{3\sqrt2}{2}$.
Section C — Short Answer (3 marks)
  1. $\sqrt3+\sqrt2$.
  2. $2-\sqrt3$.
  3. $\sqrt6-1$.
  4. $3-2\sqrt2$.
Section D — Long Answer (5 marks)
  1. $4+\sqrt{15}$.
  2. $a=1,\ b=1$.
Generated by Vidaara.org · Assignment VID-M09-01-RAT-01 · vidaara.org