In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:$ u^{2}=\frac{17}{4} $

Given:

\( u^{2}=\frac{17}{4} \)

To do:

We have to find whether $u$ 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.

$u^2=\frac{17}{4}$

$\Rightarrow u^2=(\sqrt{\frac{17}{4}})^2$

$\Rightarrow u=\frac{\sqrt{17}}{2}$

$\sqrt{17}$ is an irrational number.

$\Rightarrow u=\frac{\sqrt{17}}{2}$ is an irrational number.

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