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Prove that \frac{1}{\sqrt{3}} is irrational.
CBSE | Class 10 | Exercise 1D | Maths | Real Numbers | RS Aggarwal
Prove that \frac{1}{\sqrt{3}} is irrational.

Answer:

Consider,  \frac{1}{\sqrt{3}} be rational.

\frac{1}{\sqrt{3}}=\frac{a}{b} , where a, b are positive integers having no common factor other than 1

∴√3 = \frac{b}{a}

Since a, b are non-zero integers, \frac{b}{a} is rational.

Thus, equation shows that √3 is rational.

This contradicts the fact that √3 is rational.

The contradiction arises by assuming √3 is rational.

Thus, \frac{1}{\sqrt{3}}  is irrational.

 

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