RD Sharma Solutions for Class 9 Chapter 3 Rationalisation Exercise 3.2

Chapter 3 Rationalisation RD Sharma Solutions Exercise 3.2 Class 9 Maths

Chapter Name	RD Sharma Chapter 3 Rationalisation Exercise 3.2
Book Name	RD Sharma Mathematics for Class 10
Other Exercises	Exercise 3.1
Related Study	NCERT Solutions for Class 10 Maths

Exercise 3.2 Solutions

1. Rationalise the denominator 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) 3√5/5
(ii) 3√5/10
(iii) √3/6
(iv) √10/5
(v) (√6 + √2)/2
(vi) (√6 + √5)/3 
(vii) 3√10/5

2. Find the value of three places of decimals of each of the following. 
√2 = 1.414, √3 = 1.732, √5 = 2.236  and √10 = 3.162.
(i) 2/√3
(ii) 3/√10 
(iii) (√5 + 1)/√2
(iv) (√10+ √15)/√2
(v) (2 + √3)/3
(vi) (√2 - 1)/√5

Solution

Given that √2 = 1.414, √3 = 1.732, √5 = 2.236  and √10 = 3.162.

3. Express each one of the following with rational denominator: 

(i) 1/(3+ √2)
(ii) 1/(√6 - √5)
(iii) 16/(√41 - 5)
(iv) 30/(5√3 - 3√5)
(v) 1/(2√5 - √3)
(vi) (√3 + 1)/(2√2 - √)
(vii) (6 - 4√2)/(6 + 4√2)
(viii) (3√2 + 1)/(2√5 - 3)
(ix) b²/√(a² + b²)+ a

Solution 

4. Rationalize the denominator and simplify : 
(i) (√3 - √2)/(√3 + √2)
(ii) (5 + 2√3)/(7 + 4√3)
(iii) (1 + √2)/(3 - 2√2)
(iv) (2√6 - √5)/(3√5 - 2√6)
(v) (4√3 + 5√2)/(√48 + √18)
(vi) (2√3 - √5)/(2√2 + 3√3)

Solution 

5. Simplify : 

(i) (3√2 - 2√3)/(3√2 + 2√3) + √12/(√3 - √2)
(ii) (√5 + √3)/(√5 - √3) + (√5 - √3)/(√5 + √3)

(iii) (7 + 3√5)/(3 + √5) - (7 -3√5)/(3 - √5)
(iv) 1/(2 + √3) + 2/(√5 - √3) + 1/(2 - √5)
(v) 2/(√5 + √3) + 1/(√3 + √2) - 3/(√5 + √2)

Solution

6. In each of the following determine rational numbers a and b : 

(i)  (√3 - 1)/(√3 + 1) = a - b√3
(ii) (4 + √2)/(2 + √2) = a - √b
(iii) (3+ √2)/(3 - √2) = a + b√2
(iv) (5 + 3√3)/(7 + 4√3) = a + b√3
(v) (√11 - √7)/(√11 + √7) = a - b√77
(vi) (4 + 3√5)/(4 - 3√5) = a + b√5

Solution

7. If x = 2 + √3, find the value of  x³ + 1/x³     . 

Solution

Given x = 2 + √3 and given to find the value of x³ + 1/x³   . 
We have x = 2 + √3 
⇒ 1/x =1/(2 + √3)
Rationalization factor for 1/(a + √b) is a - √b

8. If x = 3 + √8, find the value of x² + 1/x² .

Solution

9. Find the value of 6/(√5 - √3), it being given that √3 = 1.732 and √5 = 2.236.

Solution

Given to find the value of 6/(√5 - √3)

10. Find the values of each of the following correct to three places of decimals, it being given that √2 = 1.4142, √3 = 1.732, √5 = 2.2360, √6 = 2.4495 and √10 = 3.162 

(i) (3 - √5)/(3 +2√5) 

Solution

11. If x = (√3 + 1)/2, find the value of 4x³ + 2x² – 8x + 7.

Solution