Define an irrational number.

Define the irrational numbers. Give examples.

Negation of an irrational number is an irrational number.

Multiplication of a non-zero rational number with an irrational number is 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.

Prove the following by contradiction : "The sum of a rational and irrational number is an irrational number ."

The sum; Difference;poduct and quotient of two irrational numbers need not be an irrational number.

Assertion : 5-sqrt(2)=5-1.414=3.586 is an irrational number . Reason : The difference of a rational number and an irrational number is an irrational number .

Assertion(A): sqrt(a) is an irrational number, when a is a prime number. Reason (R):Square root of any prime number is an irrational number.

Give an example of each,of two irrational numbers whose: difference is a rational number.difference is an irrational number. sum is a rational number.sum is an irrational number.product is a rational number.product is an irrrational number.quotient is a rational number.quotient is an irrational number.

Prove that the sum of or the difference between, a rational number alpha and an irrational number beta is an irrational number.