Mathematics · Real Numbers · NCERT Examples

Example 7

A complete, independently verified solution for NCERT Example 7.

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Mathematics · Chapter 1 · NCERT Examples

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NCERT Example

Example 7

irrational numbers · proof by contradiction

Show that 3√2 is irrational.

Solution

Suppose 3√2 = r for a rational number r.

2=r3\sqrt2=\frac r3

The right side would be rational, contradicting the irrationality of √2.

Final answer

Therefore, 3√2 is irrational.

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