## 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.

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Question 6.

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Question 7.

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Question 8.

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Question 9.

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Question 10.

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Question 11.

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Question 12.

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Question 13.

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Question 14.

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Question 15.

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Question 16.

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Question 17.

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Question 18.

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Question 19.

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Question 20.

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Question 21.

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Question 22.

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Question 23.

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Question 24.

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Question 25.

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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