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Prove that of the Numbers `3 Sqrt(7)` Is Irrational: - Mathematics

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Prove that of the numbers  `3 sqrt(7)`  is irrational:

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Solution

Let `3 sqrt(7)` be rational.
`1/3 ×3 sqrt(7)= sqrt(7)` = rational          [∵Product of two rational is rational]
This contradicts the fact that `sqrt(7)` is irrational.
The contradiction arises by assuming `3 sqrt(7)` is rational.
Hence, `3 sqrt(7)` is irrational.

Concept: Concept of Irrational Numbers
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