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

a be a rational number and b be an irrational number then ab necessarily will be an irrational number.
Example: 6 is a rational number but $\sqrt{5}$ is irrational. And 6 $\sqrt{5}$ is also an irrational number.

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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.

a be a rational number and b be an irrational number then ab necessarily will be an irrational number. Example: 6 is a rational number but 5 is irrational. And 65 is also an irrational number.

a be a rational number and b be an irrational number then ab necessarily will be an irrational number.
Example: 6 is a rational number but $\sqrt{5}$ is irrational. And 6 $\sqrt{5}$ is also an irrational number.