Express each one of the following with rational denominator:
(i)
(ii) 
(iii)
(iv)
(v) 
(vi)
(vii) 
(viii)
(ix)
(i) we have 
rationalising factor of denominator is 3-√2
(ii) we have 
rationalising factor of denominator is 
= 
(iii) we have 
rationalising factor of denominator is 
= 
= 
=
(iv) we have 
rationalising factor of 
= 
= 
= 
=
(v) we have 
rationalising factor of 
(vi) we have 
rationalising factor of 
(vii) we have 
rationalising factor of 
= 
Because; 
(viii) we have 
rationalising factor of 
(ix) we have 
rationalising factor of 
3