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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