Question
Classify the following number as rational or irrational:$3\sqrt{7}$
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Answer
Let $3\sqrt7$ be rational.
$\therefore\frac{1}3{}\times3\sqrt{7}=\sqrt{7}=$ rational $[\because$ Product of two rational is rational$]$
This contradicts the fact that $\sqrt7$ is irrational.
The contradiction arises by assuming $3\sqrt7$ is rational.
Hence, $3\sqrt7$ is irrational.
$\therefore\frac{1}3{}\times3\sqrt{7}=\sqrt{7}=$ rational $[\because$ Product of two rational is rational$]$
This contradicts the fact that $\sqrt7$ is irrational.
The contradiction arises by assuming $3\sqrt7$ is rational.
Hence, $3\sqrt7$ is irrational.
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