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