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.