 # RD Sharma Solutions for Class 9 Maths Chapter 3 Rationalisation Exercise VSAQs

RD Sharma class 9 mathematics chapter 3 exercise VSAQs Rationalisation is provided here. Our experts have designed RD Sharma Class 9 chapter 3 solutions in accordance with CBSE syllabus for class 9. Learning this chapter will also help the students to score good marks in the examination. Students can download RD Sharma exercise VSAQs by clicking on the link below.

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Question 1: Write the value of (2 + √3) (2 – √3).

Solution:

(2 + √3) (2 – √3)

= (2)2 – (√3)2

[Using identity : (a + b)(a – b) = a2 – b2]

= 4 – 3

= 1

Question 2: Write the reciprocal of 5 + √2.

Solution: Question 3: Write the rationalisation factor of 7 – 3√5.

Solution:

Rationalisation factor of 7 – 3√5 is 7 + 3√5

Question 4: If Find the values of x and y.

Solution:

[Using identities : (a + b)(a – b) = a2 – b2 and (a – b)2 = a2 + b2 – 2ab] Question 5: If x = √2 – 1, then write the value of 1/x.

Solution:

x = √2 – 1

or 1/x = 1/(√2 – 1)

Rationalising denominator, we have

= 1/(√2 – 1) x (√2 + 1)/(√2 + 1)

= (√2 + 1)/(2-1)

= √2 + 1

Question 6: Simplify Solution: [ Because: (a + b)2 = a2 + b2 + 2ab ]

Question 7: Simplify Solution: [ Because: (a – b)2 = a2 + b2 – 2ab ]

Question 8: If a = √2 +1, then find the value of a – 1/a.

Solution:

Given: a = √2 + 1

1/a = 1/(√2 + 1)

= 1/(√2 + 1) x (√2 – 1)/(√2 – 1)

= (√2 – 1)/ ((√2)2 – (1)2)

= (√2 – 1)/1

= √2 – 1

Now,

a – 1/a = (√2 + 1) – (√2 – 1)

= 2

Question 9: If x = 2 + √3, find the value of x + 1/x.

Solution:

Given: x = 2 + √3

1/a = 1/(2 + √3)

= 1/(2 + √3) x (2 – √3)/(2 – √3)

= (2 – √3)/ ((2)2 – (√3)2)

= (2 – √3)/(4-3)

= (2 – √3)

Now,

x + 1/x = (2 + √3) + (2 – √3)

= 4

Question 10: Write the rationalisation factor of √5 – 2.

Solution:

Rationalisation factor of √5 – 2 is √5 + 2

Question 11: If x = 3 + 2√2, then find the value of √x – 1/√x.

Solution: ## RD Sharma Solutions for Class 9 Maths Chapter 3 Exercise VSAQs

RD Sharma Solutions Class 9 Maths Chapter 3 Rationalisation Exercise VSAQs is based on the following topics:

• Use of some important algebraic identities
• Rationalisation of denominator