Question
Classify the following number as rational or irrational:$\sqrt{6}$
✓
Answer
Let $\sqrt6=\sqrt2\times\sqrt3$ be rational.
Hence, $\sqrt2,\ \sqrt{3}$ are both rational.
This contradicts the fact that $\sqrt2,\ \sqrt{3}$ are irrational.
The contradiction arises by assuming $\sqrt6$ is rational.
Hence, $\sqrt6$ is irrational.
Hence, $\sqrt2,\ \sqrt{3}$ are both rational.
This contradicts the fact that $\sqrt2,\ \sqrt{3}$ are irrational.
The contradiction arises by assuming $\sqrt6$ is rational.
Hence, $\sqrt6$ is irrational.
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