Giving reason in each case, show that each of the following numbers is irrational.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(i) 
We cannot simplify 
Hence 4 + 
is an irrational number.
(ii) 
= 
We can’t simplify 
Hence it is an irrational number.
(iii) 
We can’t simplify 
Hence it is an irrational number.
(iv) 
= 
We can’t simplify 
Hence it is an irrational number.
(v) 
We cannot simplify 
Hence it is an irrational number.
(vi) 
We cannot simplify 
Hence it is an irrational number.
5