In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:$ x^{2}=5 $

Given:

\( x^{2}=5 \)

To do:

We have to find whether $x$ represents a rational number or an irrational number.

Solution:  

A rational number can be expressed in either terminating decimal or non-terminating recurring decimals and an irrational number is expressed in non-terminating non-recurring decimals.

$x^2=5$

$\Rightarrow x^2=(\pm \sqrt{5})^2$

$\Rightarrow x=\pm \sqrt{5}$

$\sqrt{5}$ is an irrational number.

Therefore, \( x \) is an irrational number.       

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Updated on: 10-Oct-2022

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