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What are irrational numbers? How do they differ from rational numbers? Give examples.
Irrational number:- A number which can’t be expressed as an terminating decimal or recurring decimal and fractional form is called irrational.
Ex: π, (3.1415926535),
Irrational number is different from Rational number because Rational number is a number which can be expressed as fractional form or terminating decimal form is called rational number. It is exactly the opposite of Irrational number.
Ex:- 5 ,
State in each case, whether the given statement is true 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 an 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.
(viii) Every real number is either rational or irrational.
(ix) is irrational and is rational.