If x is rational and y is irrational, then show that (x + y) is always irrational.

Match the following columns:

The correct answer is:

(a)-……., (b)-……., (c)-……., (d)-…….,

Give an example of two irrational numbers whose sum as well as the product is rational.

Is the product of a rational and an irrational number always irrational?

Give an example.

Given an example of a number x such that x² is an irrational number and x⁴ is a rational number.