Let r be a rational number and x be an irrational number. Use proof by contradiction to show that `r + x` is an irrational number.

sqrt5 is an irrational number.

Which one is an irrational number?

Let x and y be rational numbers. Show that xy is a rational number.

Insert a rational number and an irrational number between the following: 2 and 3

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

Insert a rational and an irrational number between 3 and 4.

Insert a rational number and an irrational number between the following: 0 and 0.1

Explain, how irrational number differ from rational number.

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.