√7 is irrational number.
Rational numbers are those which can be expressed as ratio of two integers i.e. p/q where p,q are two integers and q≠0.
Simply, finite decimal numbers, infinite recurring decimal numbers are also rational numbers.
Irrational number is not rational number which can not be expressed as the ratio of any two integers. Simply infinte non recurring decimal numbers fall in irrational number category.
e.g. √2,√3,√5,√7,π,e are also example of irrational numbers.
Now checking all options,
(A) 0.020202... is rational number as it can be expressed as infinite recurring decimal numbers and also can be expressed as ratio of two integers 0.020202...=2/99
(B) 0.8 is rational number as it can be expressed as finite decimal numbers and also can be expressed as ratio of two integers 0.8=4/5
(C) √7 is irrational number as it can not be expressed as the ratio of two integers.
(D) 0.3333...... is rational number as it can be expressed as infinite recurring decimal numbers and also can be expressed as ratio of two integers 0.333...=1/3
Therefore √7 is irrational number.
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