Prove that following statements.
The sum of an irrational number and a rational number is always irrational.

The product of a non-zero rational number and an irrational number is irrational.

The square of an irrational number is always rational.

Check the validity of the statement given below by the method given against it. The sum of an irrational number and a rational number is irrational.

Check the validity of the statement given below by the method given against it:- p: The sum of an irrational number and a rational number is irrational (by contradiction method).

Which one of the following statement is true? (i) The sum of two irrational numbers is always an irrational number. (ii) The sum of two irrational numbers is always a rational number. (iii) The sum of two irrational numbers may be a rational number or irrational number. (iv) The sum of two irrational numbers is always an integer.

Write the difference of an irrational and a rational number.

The product of a non-zero rational and irrational number is

Irrational numbers are real numbers also.

All the rational numbers are irrational also.

Explain, how irrational number differ from rational number.