Define an irrational number.

Give an example of each, of two irrational numbers whose: (i) difference is a rational number. (ii) difference is an irrational number. (iii) sum is a rational number. (iv) sum is an irrational number. (v) product is a rational number. (vi) product is an irrational number. (vii) quotient is a rational number. (viii) quotient is an irrational number.

Check the validity of the statement given below by contradiction method. 'Sum of a rational number and an irrational number is an irrational number.'

Are the following pairs of statements are negation of each other: The number x is not a rational number. The number x is not an irrational number.

For real numbers x and y, define xRY if and only if x - y + sqrt(2) is an irrational number. Then the relation R is

The product of two irrational numbers is an irrational number (True/false).

The sum of two irrational numbers is an irrational number (True/false).

Give examples of two irrational numbers the product of which is: a rational number (ii) an irrational number

Show that 2-sqrt(3) is an irrational number. Given sqrt(3) is irrational.

Find whether the following statements are true or false. (i) Every real number is either rational or irrational. (ii) pi is an irrational number. (iii) Irrational numbers cannot be represented by points on the number line.

If a is an irrational number which is divisible by b, then the number b