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.