i) 
ii) 
iii) 
iv) 
v) 
vi) √π
to be a surd:- 'n' should be a positive integer greater than 1
- 'a' should be a positive rational number
-
should be an irrational number
i)
=
(32)1/5 =
(25)1/5 = 2
→ a rational number.
Condition 'c' is not satisfied.
So is
not a surd.
ii)
=
(4)1/4 = (22)1/4 = 21/2 = √2 →
irrational number.
All three conditions are satisfied.
So is a surd.
iii)
a = – 10 is not a positive rational number.
Condition 'b' is not satisfied.
So is not a surd.
iv)
n = 4 but a = √5 is not a positive rational number.
So we may tend to conclude it as "not a surd".
But let us rewrite the term.
=
=
(51/2)1/4 = 51/8 = 
Now n = 8, a = 5 and is an irrational number.
i.e, all the three conditions are satisfied.
So is a surd.
v)
= 
= 22/7
n = 2, a = 484/49 but √a = 22/7 which is a rational number.
Condition 'c' is not satisfied.
So
is not a surd.
vi) √π
n = 2 and a = π
Since π is an irrational number, condition 'b' is not satisfied.
Hence √π is not a surd.