In the following equations, find which variables x, y, z etc. represent rational or irrational numbers:
(i) x2 = 5 (ii) y2 = 9 (iii) z2 = 0.04 (iv) u2 =
(v) v2 = 3 (vi) w2 = 27 (vii) t2 = 0.4
(i) We have,
x2 = 5
Taking square root on both sides,
= 
2 = 
= x = 
is not a perfect square root, so it is an irrational number.
(ii) We have,
y2 = 9
y = 
= 3 = 
can be expressed in the form of 
, so it is a rational number.
(iii) We have,
z2 = 0.04
Taking square root on both the sides, we get,
2 = 
z = 
= 0.2 = 
= 
z can be expressed in the form of 
, so it is a rational number.
(iv) We have,
u2 = 
Taking square root on both the sides, we get
2 = 
u = 
Quotient of an rational number is irrational, so u is an irrational number.
(v) We have,
v2 = 3
Taking square roots on both the sides, we get,
2 = 
v = 
is not a perfect square root, so v is an irrational number.
(vi) We have,
w2 = 27
Taking square roots on both the sides, we get,
2 = 
w = 
= 3
Product of a rational number and an irrational number is irrational number. So, it is an irrational number.
(vii) We have,
t2 = 0.4
Taking square roots on both the sides, we get,
2 = 
= 
= 
Since, quotient of a rational number and an irrational number is irrational number, so t is an irrational number.