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Question
Prove that `1/sqrt (3)` is irrational.
Solution
Let `1/sqrt (3)` be rational.
∴ `1/sqrt (3) = a/b` , where a, b are positive integers having no common factor other than 1
∴` sqrt(3) = b/a` ….(1)
Since a, b are non-zero integers, `b/a`is rational.
Thus, equation (1) shows that `sqrt (3)` is rational.
This contradicts the fact that `sqrt(3)` is rational.
The contradiction arises by assuming `sqrt(3)` is rational.
Hence, `1/sqrt (3)` is irrational.
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