(i) We have
x2 = 5
Taking square root on both sides.
=> √x2 = √5
=> x = √5
√5 is not a perfect square root, so it is an irrational number.
(ii) We have
y2 = 9
=> y = √9
=3
=3/1
√9 can be expressed in the form of p/q, so it a rational number.
(iii) We have
z2 = 0.04
Taking square root on both sides, we get,
√z2 =√0.04
=> z = √0.04
= 0.2
= 2/10
= 1/5
z can be expressed in the form of p/q, so it is a rational number.
(iv) We have
u2 =17/4
Taking square root on both sides, we get,
√u2 =√17/4
=> u = √17/2
Quotient of an irrational and a rational number is irrational, so u is an irrational number.
(v) We have
v2 = 3
Taking square root on both sides, we get,
√v2 = √13
=> v = √3
√3 is not a perfect square root, so y is an irrational number.
(vi) We have
w2 = 27
Taking square root on both sides, we get,
√w2 = √27
=> w = √3 x 3 x 3
=3√3
Product of a rational and an irrational is irrational number, so w is an irrational number.
(vii) We have
t2 = 0.4
Taking square root on both sides, we get
√t2 = √0.4
=> t = √4/10
= 2/√10
Since, quotient of a rational and an irrational number is irrational number, so t is an irrational number.