Let $x$ be rational and $y$ be irrational. Is $xy$ necessarily irrational?Justify.

Solution:

No because $x$ can be 0 and any real number multiply by 0 is 0.

Example: $0\times\sqrt{2} = 0$

The final answer is 0 which is Rational.

In other cases where $x$ is not 0, then $xy$ is irrational.

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Updated on: 10-Oct-2022

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