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Mathematics · Real Numbers · NCERT Examples

Example 6

A complete, independently verified solution for NCERT Example 6.

Mathematics · Chapter 1 · NCERT Examples

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NCERT Example

Example 6

irrational numbers · proof by contradiction

Show that 5 − √3 is irrational.

Solution

Suppose 5 − √3 = r for a rational number r.

3=5−r\sqrt3=5-r

The right side would be rational, contradicting the irrationality of √3.

Final answer

Therefore, 5 − √3 is irrational.