Let a be a rational number and b be an irrational number. Is ab necessarily an irrational number ? Justify your answer with an example.

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Solution

If a is a rational number and b is an irrational number.
ab is an irrational number except for a =0
for a =0 ; ab is a rational number.
otherwise multiplication of one rational and one irrational number is an irrational number.

example :

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Let a be a rational number and b be an irrational number. Is ab necessarily an irrational number ? Justify your answer with an example.

If a is a rational number and b is an irrational number. ab is an irrational number except for a =0 for a =0 ; ab is a rational number. otherwise multiplication of one rational and one irrational number is an irrational number. example :

If a is a rational number and b is an irrational number.
ab is an irrational number except for a =0
for a =0 ; ab is a rational number.
otherwise multiplication of one rational and one irrational number is an irrational number.

example :