RD Sharma Solutions for Class 9 Mathematics Chapter 3 Exercise 3.2 Rationalisation are provided here. The subject experts at BYJU’S have designed RD Sharma Class 9 Chapter 3 solutions in accordance with the latest CBSE syllabus for Class 9. Learning this chapter will help the students to score good marks in the annual examination. Students can download RD Sharma Solutions for Class 9 Chapter 3 Exercise 3.2 by clicking on the link below.
RD Sharma Solutions for Class 9 Maths Chapter 3 Rationalisation Exercise 3.2
Question 1: Rationalise the denominators of each of the following (i – vii):
(i) 3/ √5 (ii) 3/(2 √5) (iii) 1/ √12 (iv) √2/ √5
(v) (√3 + 1)/ √2 (vi) (√2 + √5)/ √3 (vii) 3 √2/ √5
Solution:
(i) Multiply both the numerator and denominator with the same number to rationalise the denominator.
= 3√5/5
(ii) Multiply both the numerator and denominator with the same number to rationalise the denominator.
(iii) Multiply both the numerator and denominator with the same number to rationalise the denominator.
(iv) Multiply both the numerator and denominator with the same number to rationalise the denominator.
(v) Multiply both the numerator and denominator with the same number to rationalise the denominator.
(vi) Multiply both the numerator and denominator with the same number to rationalise the denominator.
(vii) Multiply both the numerator and denominator with the same number to rationalise the denominator.
Question 2: Find the value to three places of decimals of each of the following. It is given that
√2 = 1.414, √3 = 1.732, √5 = 2.236 and √10 = 3.162
Solution:
Question 3: Express each one of the following with a rational denominator:
Solution:
Using identity: (a + b) (a – b) = a2 – b2
(i) Multiply and divide the given number by 3−√2
(ii) Multiply and divide the given number by √6 + √5
(iii) Multiply and divide the given number by √41 + 5
(iv) Multiply and divide the given number by 5√3 + 3√5
(v) Multiply and divide the given number by 2√5 + √3
(vi) Multiply and divide the given number by 2√2 + √3
(vii) Multiply and divide the given number by 6 – 4√2
(viii) Multiply and divide the given number by 2√5 + 3
(ix) Multiply and divide the given number by √(a2+b2) – a
Question 4: Rationales the denominator and simplify:
Solution:
[Use identities: (a + b) (a – b) = a2 – b2 ; (a + b)2 = (a2 + 2ab + b2 and (a – b)2 = (a2 – 2ab + b2 ](i) Multiply both numerator and denominator by √3–√2 to rationalise the denominator.
(ii) Multiply both numerator and denominator by 7–4√3 to rationalise the denominator.
(iii) Multiply both numerator and denominator by 3+2√2 to rationalise the denominator.
(iv) Multiply both numerator and denominator by 3√5+2√6 to rationalise the denominator.
(v) Multiply both numerator and denominator by √48–√18 to rationalise the denominator.
(vi) Multiply both numerator and denominator by 2√2 – 3√3 to rationalise the denominator.
RD Sharma Solutions for Class 9 Maths Chapter 3 Rationalisation Exercise 3.2
RD Sharma Solutions Class 9 Maths Chapter 3 Rationalisation Exercise 3.2 are based on the rationalisation of the denominator. In this process, we move a root from the bottom of a fraction to the top to simplify the fraction.
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