RD Sharma Class 9th Solutions Chapter 3 Rationalisation

RD Sharma Class 9 Solutions Chapter 3 Rationalisation

RD Sharma Class 9 Chapter 3 Rationalisation Ex 3.1

Question 1.
Simplify each of the following:

Solution:

Question 2.
Simplify the following expressions:
(i) (4 + $\sqrt { 7 }$ ) (3 + $\sqrt { 2 }$ )
(ii) (3 + $\sqrt { 3 }$ )(5- $\sqrt { 2 }$ )
(iii) ( $\sqrt { 5 }$ -2)( $\sqrt { 3 }$ – $\sqrt { 5 }$ )
Solution:

Question 3.
Simplify the following expressions:
(i) (11 + $\sqrt { 11 }$ ) (11 – $\sqrt { 11 }$ )
(ii) (5 + $\sqrt { 7 }$ ) (5 – $\sqrt { 7 }$ )
(iii) ( $\sqrt { 8 }$ – $\sqrt { 2 }$ ) ( $\sqrt { 8 }$ + $\sqrt { 2 }$ )
Solution:

Question 4.
Simplify the following expressions:
(i) ( $\sqrt { 3 }$ + $\sqrt { 7 }$ )²
(ii) ( $\sqrt { 5 }$ – $\sqrt { 3 }$ )²(iii) (2 $\sqrt { 5 }$ + 3 $\sqrt { 2}$ )²
Solution:

RD Sharma Solutions Class 9 Chapter 3 Rationalisation Ex 3.2

Question 1.
Rationalise the denominators of each of the following(i – vii):

Solution:

Question 2.
Find the value to three places of decimals of each of the following. It is given that

Solution:

Question 3.
Express each one of the following with rational denominator:

Solution:

Question 4.
Rationales the denominator and simplify:

Solution:

Question 5.
Simplify:

Solution:

Question 6.
In each of the following determine rational numbers a and b:

Solution:

Question 7.

Solution:

Question 8.
Find the values of each of the following correct to three places of decimals, it being given that $\sqrt { 2 }$ = 1.4142, $\sqrt { 3 }$ = 1-732, $\sqrt { 5 }$ = 2.2360, $\sqrt { 6 }$ = 2.4495 and $\sqrt { 10 }$ = 3.162.

Solution:

Question 9.
Simplify:

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Class 9 RD Sharma Solutions Chapter 3 Rationalisation VSAQS

Question 1.
Write the value of (2 + $\sqrt { 3 }$ ) (2 – $\sqrt { 3 }$ ).
Solution:
(2+ $\sqrt { 3 }$ )(2- $\sqrt { 3 }$ ) = (2)²-( $\sqrt { 3 }$ )²{∵ (a + b) (a – b) = a² – b²}
= 4-3=1

Question 2.
Write the reciprocal of 5 + $\sqrt { 2 }$ .
Solution:

Question 3.
Write the rationalisation factor of 7 – 3 $\sqrt { 5 }$ .
Solution:
Rationalising factor of 7 – 3 $\sqrt { 5 }$ is 7 + 3 $\sqrt { 5 }$
{∵ ( $\sqrt { a }$ + $\sqrt { b }$ ) ( $\sqrt { a }$ – $\sqrt { b }$ ) = a-b}

Question 4.

Solution:

Question 5.
If x = $\sqrt { 2 }$ – 1 then write the value of $\frac { 1 }{ x }$ .
Solution:

Question 6.
If a = $\sqrt { 2 }$ + h then find the value of a – $\frac { 1 }{ a }$
Solution:

Question 7.
If x = 2 + $\sqrt { 3 }$ , find the value of x + $\frac { 1 }{ x }$ .
Solution:

Question 8.
Write the rationalisation factor of $\sqrt { 5 }$ – 2.
Solution:
Rationalisation factor of $\sqrt { 5 }$ – 2 is $\sqrt { 5 }$ + 2 as
( $\sqrt { a }$ + $\sqrt { b }$ )( $\sqrt { a }$ – $\sqrt { b }$ ) = a – b

Question 9.
Simplify : $\sqrt { 3+2\sqrt { 2 } }$ .
Solution:

Question 10.
Simplify : $\sqrt { 3-2\sqrt { 2 } }$ .
Solution:

Question 11.
If x = 3 + 2 $\sqrt { 2 }$ , then find the value of $\sqrt { x }$ – $\frac { 1 }{ \sqrt { x } }$ .
Solution:

Rationalisation Problems With Solutions PDF RD Sharma Class 9 Solutions MCQS

Mark the correct alternative in each of the following:

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.
The rationalisation factor of 2 + $\sqrt { 3 }$ is
(a) 2 – $\sqrt { 3 }$
(b) $\sqrt { 2 }$ + 3
(c) $\sqrt { 2 }$ – 3
(d) $\sqrt { 3 }$ – 2
Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.

Solution:

Question 23.

Solution:

Question 24.

Solution:

Question 25.

Solution:

RD Sharma Class 9th Solutions Chapter 3 Rationalisation Exercise 3.1
Q1 Q2 Q3 Q4

RD Sharma Class 9th Solutions Chapter 3 Rationalisation Exercise 3.2
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11

RD Sharma Class 9 Solutions

RD Sharma Class 12 Solutions	RD Sharma Class 11
RD Sharma Class 10	RD Sharma Class 9
RD Sharma Class 8	RD Sharma Class 7
CBSE Previous Year Question Papers Class 12	CBSE Previous Year Question Papers Class 10
NCERT Books	Maths Formulas
CBSE Sample Papers	Vedic Maths

English Grammar	Hindi Grammar
Textbook Solutions	Maths NCERT Solutions
Science NCERT Solutions	Social Science NCERT Solutions
English Solutions	Hindi NCERT Solutions
NCERT Exemplar Problems	Engineering Entrance Exams
Like us on Facebook	Follow us on Twitter
Watch Youtube Videos	NCERT Solutions App

RD Sharma Class 9 Solutions Chapter 3 Rationalisation

RD Sharma Class 9 Solutions Chapter 3 Rationalisation

RD Sharma Class 9 Chapter 3 Rationalisation Ex 3.1

RD Sharma Solutions Class 9 Chapter 3 Rationalisation Ex 3.2

Class 9 RD Sharma Solutions Chapter 3 Rationalisation VSAQS

Rationalisation Problems With Solutions PDF RD Sharma Class 9 Solutions MCQS

Free Resources

NCERT Solutions

Quick Resources