Prove or disprove that if a and b are rational numbers, then a^{b} is also

opatovaL 2021-09-16 Answered
Prove or disprove that if a and b are rational numbers, then ab is also rational.
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aprovard
Answered 2021-09-17 Author has 94 answers

Given statement: If a and b are rational numbers, then ab is also rational.
The given statement is false, which will be disproven using a counterexample.
Counterexample
If a=1 and b=12, we then obtain (1)12=1 which is not rational number (it is called an imaginary number) and thus ab is not necessarily rational.
Result:
Statement is false, one counterexample is for a=-1 and b=12.

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