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Question
Prove that of the numbers `3 + sqrt (2)` is irrational:
Solution
Let `3 + sqrt (2)` be rational.
Hence, 3 and `3 + sqrt (2)` are rational.
∴ `3 + sqrt (2)` – `3=sqrt (2)` = rational [∵Difference of two rational is rational]
This contradicts the fact that `sqrt (2)` is irrational.
The contradiction arises by assuming `3 + sqrt (2)` is rational.
Hence, `3 + sqrt (2)` is irrational.
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