# 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