The multiplication of a rational number 'x' and an irrational number 'y' is

Multiplication of rational number

The product of a rational number and an irrational number is

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

Write a rational number and an irrational number between 1 and 2.

If x be a rational number and y be an irrational number, then :

State, in each case, whether the given statements is ture or false. (i) The sum of two rational numbers is rational. (ii) The sum of two irrational numbers is irrational. (iii) The product of two rational numbers is rational. (iv) The product of two irrational numbers is irrational. (v) The sum of a rational number and irrational number is irrational. (vi) The product of a nonzero rational number and an irrational number is a rational number. (vii)Every real number is rational or irrational. (viii) Every number is either rational or irrational. (ix) pi is irrational and (22)/(7) is rational.

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 .

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

The square of an irrational number is always a rational number