In this chapter, we provide RD Sharma Solutions for Class 9 Chapter 3 Rationalisation Maths for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Class 9 Chapter 3 Rationalisation Maths pdf, free RD Sharma Solutions for Class 9 Chapter 3 Rationalisation Maths book pdf download. Now you will get step by step solution to each question.

## 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) = a^{2} – b^{2}}

= 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+2sqrt { 2 } }).

Solution:

Question 10.

Simplify : (sqrt { 3-2sqrt { 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.

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Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

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Question 14.

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Question 15.

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Question 16.

Solution:

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.

Solution:

Question 22.

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Question 23.

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Question 24.

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Question 25.

Solution:

**All Chapter RD Sharma Solutions For Class 9 Maths**

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