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# Class 9 RD Sharma Solutions – Chapter 3 Rationalisation- Exercise 3.2 | Set 2

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

(i) (ii) (iii) (iv) (v) (vi) Solution:

(i) We know that rationalisation factor for . We will multiply numerator and denominator of the given expression , to get On equating rational and irrational terms, we get Hence, we get a = 2, b = 1

(ii) We know that rationalisation factor for . We will multiply numerator and denominator of the given expression , to get On equating rational and irrational terms, we get Hence, we get a = 3, b = 2

(iii) We know that rationalisation factor for . We will multiply numerator and denominator of the given expression, to get On equating rational and irrational terms, we get Hence, we get a = , b = (iv) We know that rationalisation factor for . We will multiply numerator and denominator of the given expression , to get On equating rational and irrational terms, we get Hence, we get a = -1, b = 1

(v) We know that rationalisation factor for . We will multiply numerator and denominator of the given expression , to get On equating rational and irrational terms, we get Hence, we get a = , b = (vi) We know that rationalisation factor for . We will multiply numerator and denominator of the given expression , to get On equating rational and irrational terms, we get Hence, we get a = , b = ### Question 7. If , find the value of Solution:

We know that . We have to find the value of As Therefore, We know that rationalization factor for . We will multiply numerator and denominator of the given expression to get, Putting the value of , we get Hence the value of the given expression is 52.

### Question 8. If . Find the value of Solution:

We know that . We have to find the value of Therefore, We know that rationalization factor for .

We will multiply numerator and denominator of the given expression to get, Putting the value of We get, Hence the given expression is simplified to 34.

### Question 9. Find the value of , it being given that Solution:

We know that for rationalization factor we will multiply denominator and numerator of the given expression to get, Putting the values of we get, Hence, value of the given expression is 11.904.

### Question 10. Find the value of each of the following correct to three place of decimals, it being given that (i) (ii) Solution:

(i) We know that rationalization factor for We will multiply numerator and denominator of the given expression to get Putting the values of We get Hence, the given expression is simplified to 0.102.

(ii) We know that rationalization factor for We will multiply numerator and denominator of the given expression to get Putting the values of We get Hence, the given expression is simplified to 14.071.

### Question 11. If , find the value of Solution:

We have, It can be simplified as On squaring both sides, we get The given equation can be rewritten as Therefore, we have Hence, the value of given expression is 10.

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