## 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 : \(\sqrt { 3+2\sqrt { 2 } }\).

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.

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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