Question

In the following equations, find whether variables $u$ represents rational or irrational numbers
$u^2=\frac{17}{4}$

Answer 1

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

$\Rightarrow u=\sqrt{\frac{17}{4}}$

$\Rightarrow u=\frac{\sqrt{17}}{2}=\frac{1}{2}\times \sqrt{17}$

Here$\frac{1}{2}$ is a rational number and $\sqrt{17}$ is an irrational number

We know that the product of rational with irrational number is an irrational number

Hence, $u$ represents an irrational number.