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+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.

Solution:

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.

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Question 22.

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Question 23.

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Question 24.

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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