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

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

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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