In the following equations, find whether variables x, y, z etc. represent rational or irrational numbers.

i. x² = 7 ii. y² = 16

iii. z² = 0.02 iv.

v. w² = 27 vi. t⁴ = 256

i. x² = 7

⇒ x = √7

Here, √7 is an irrational number.

∴ x is an irrational number.

ii. y² = 16

⇒ y = √16 = ±4

Here, 4 is a rational number.

∴ y is a rational number.

iii. z² = 0.02

⇒ z = √0.02

Here, √0.02 is an irrational number.

∴ z is an irrational number.

iv. u² =

⇒ u = =

Here, √17 is an irrational number and 2 is a rational number.

We know that division of a rational number and an irrational number gives an irrational number.

∴ u is an irrational number.

v. w² = 27

⇒ w = √27 = 3√3

Here, √3 is an irrational number.

∴ w is an irrational number.

vi. t⁴ = 256

⇒ t = = = 4

Here, 4 is a rational number.

∴ t is a rational number.