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Prove that of the Numbers `Sqrt (6) ` is Irrational: - Mathematics

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Prove that of the numbers `sqrt (6) ` is irrational:

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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.

Concept: Concept of Irrational Numbers
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