alleryLet $r$ be a non-zero rational number and $x$ be an irrational number. Which of the following must be irrational?
AOnly $r+x$
BOnly $rx$
CBoth $r+x$ and $\frac{x}{r}$
DNeither $r+x$ nor $rx$
Answer & Solution
Correct answer: C. Both $r+x$ and $\frac{x}{r}$
The notes state that the sum of a rational and an irrational number is irrational.
They also state that the product and quotient of a non-zero rational number and an irrational number are irrational.
**Hence both $r+x$ and $x/r$ are irrational.**
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