RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions for Class 9 Mathematics

Created by: Abhishek Kapoor

Class 9 : RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

The document RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
All you need of Class 9 at this link: Class 9

1. Rationalize the denominator of each of the following:

(i) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
(ii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (iii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (iv)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (v)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (vi)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (vii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Solution: (i) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev  For rationalizing the denominator, multiply both numerator and denominator with  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(ii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev  For rationalizing the denominator, multiply both numerator and denominator with RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev  For rationalizing the denominator, multiply both numerator and denominator with  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iv)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev For rationalizing the denominator, multiply both numerator and denominator with  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(v)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev For rationalizing the denominator, multiply both numerator and denominator with  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(vi)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev For rationalizing the denominator, multiply both numerator and denominator with  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(vii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev  For rationalizing the denominator, multiply both numerator and denominator with  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev


2. Find the value to three places of decimals of each of the following. It is given that RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev  = 1.414,RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 1.732,RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev  = 2.236, RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 3.162.

(i) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
(ii) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
(iii) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
(iv) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
(v) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
(vi) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Solution: Given,  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev  = 1.414,RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 1.732,RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev  = 2.236, RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 3.162.

(i) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(ii) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iii) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iv) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(vi) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev


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

(i) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
(ii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (iii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (iv)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (v)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (vi) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (vii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (viii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
 (ix)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Solution: (i) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(ii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev 

As we know, (a + b) (a - b) = (a2 − b2) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iv)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2) =  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(v)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2) =  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(vi) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2) = RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(vii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev As we know , (a - b)2 = (a2−2×a×b+b2) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(viii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2) =  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(ix)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev


4. Rationalize the denominator and simplify: 

(i)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(ii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iv)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(v)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(vi)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Solution: (i)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev As we know , (a - b) 2 = (a2−2×a×b+b2) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(ii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2) =  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iv)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

 As we know, (a + b) (a - b) = (a2−b2) = RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(v)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2) =  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(vi)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev
RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

5. Simplify: 

(i) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(ii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iii)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iv)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(v)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

 Solution: (i) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev and the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

 Now, (a + b) (a - b) = (a2−b2) =  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev 

As we know , (a - b)2 = (a2−2×a×b+b2) =  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(ii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev and the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev =  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

 

Now as we know, (a + b) (a - b) = (a2−b2), (a - b)2 = (a2−2×a×b+b2) and (a+b)2 = (a2+2×a×b+b2)

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iii)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev and the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Now as we know, (a + b) (a - b) = (a2−b2) =  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iv)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev, and the rationalizing factor RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Since, (a + b) (a - b) = (a2−b2) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(v)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev  Rationalizing the denominator by multiplying both numerator and denominator with  the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev and the rationalizing factor RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev 

Since, (a + b) (a - b) = (a2−b2) =  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev


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

(i) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(ii)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iv)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(v)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(vi)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Solution:   (i) Given, RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor 

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

On comparing the rational and irrational parts of the above equation, we get, a = 2 and b = 1

(ii)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

On comparing the rational and irrational parts of the above equation, we get,

a = 3 and b = 2

(iii)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

On comparing the rational and irrational parts of the above equation, we get,

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(iv)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = ( RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

On comparing the rational and irrational parts of the above equation, we get,

a = -1 and

b = 1

(v)  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2) =  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

On comparing the rational and irrational parts of the above equation, we get,

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(vi)   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

On comparing the rational and irrational parts of the above equation, we get,

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

7. If x = 2 + RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev find the value of RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Solution:  Given, x = 2 + RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev To find the value of  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

We have,  x = 2 + RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev 

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Since, (a + b) (a - b) = (a2−b2)

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

We know that,  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Putting the value of  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev in the above equation, we get,

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev


8. If x = 3 + RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev find the value of RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Solution:   Given, x = 3 +  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

To find the value of   RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev We have,  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Since, (a + b) (a - b) = (a2−b2)

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev


9. Find the value of RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev it being given that RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 1.732 and RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev= 2.236. 

Solution. Given,  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Since, (a + b) (a - b) = (a2−b2) = RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 3(2.236+1.732) = 3(3.968) = 11.904 


10. Find the values of each of the following correct to three places of decimals, it being given that RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 1.414,RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 1.732,RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 2.236,RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 2.4495,RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 3.162

Solution. (i) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Since, (a + b) (a - b) = (a2−b2) =RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

(ii) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor  RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

As we know, (a + b) (a - b) = (a2−b2) RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRevRD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev = 7 + 7.07 = 14.07 


11. If x = RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev find the value of 4x3+2x2−8x+7.

Solution: Given, RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev 

and given to find the value of 4x3+2x2−8x+7

RD Sharma Solutions Ex-3.2, Rationalisation, Class 9, Maths Class 9 Notes | EduRev

Now, squaring on both the sides, we get, (2x−1)2 = 3

4x2−4x+1 = 3

4x2−4x+1−3 = 0

4x2−4x−2 = 0

2x2−2x−1 = 0

Now taking 4x3+2x2−8x+7

2x(2x2−2x−1)+ 4x2+2x+2x2−8x+7

2x(2x2−2x−1)+ 6x2−6x+7

As, 2x2−2x−1=0

2x(0)+3(2x2−2x−1))+7+3

0+3(0)+10

10

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