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Which statement correctly justifies that $3\sqrt{2}$ is irrational?
AIf $3\sqrt{2}$ were rational, then dividing by the non-zero rational number 3 would make $\sqrt{2}$ rational, which is impossible.
B$3\sqrt{2}$ is irrational because 3 is prime.
C$3\sqrt{2}$ is irrational because all products are irrational.
D$3\sqrt{2}$ is irrational because $\sqrt{2}>3$.
Answer & Solution
Correct answer: A. If $3\sqrt{2}$ were rational, then dividing by the non-zero rational number 3 would make $\sqrt{2}$ rational, which is impossible.
Assume $3\sqrt{2}$ is rational. Since 3 is a non-zero rational number, dividing by 3 would imply $\sqrt{2}$ is rational. But $\sqrt{2}$ is irrational, so the assumption is false and $3\sqrt{2}$ is irrational.
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