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