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Question
Prove that of the numbers `sqrt (6) ` is irrational:
Solution
Let `sqrt(6) = sqrt(2) × sqrt(3)` be rational.
Hence, `sqrt(2) , sqrt(3)` are both rational.
This contradicts the fact that `sqrt( 2) , sqrt(3 )` are irrational.
The contradiction arises by assuming `sqrt(6)` is rational.
Hence, `sqrt(6)` is irrational.
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