In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:$ v^{2}=3 $
Given:
\( v^{2}=3 \)
To do:
We have to find whether $v$ 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.
$v^2=3$
$\Rightarrow v^2=(\sqrt{3})^2$
$\Rightarrow v=\sqrt{3}$
$\sqrt{3}$ is an irrational number.
Therefore, \( v \) is an irrational number.
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