Answer
$p(8)=\frac{\sqrt{70}}{20}$
$p(8)\approx 0.42$
Work Step by Step
The given function is
$\Rightarrow p(x)=\sqrt{\frac{x-1}{5x}}$
Substitute $8$ for $x$.
$\Rightarrow p(8)=\sqrt{\frac{8-1}{5(8)}}$
Simplify.
$\Rightarrow p(8)=\sqrt{\frac{7}{40}}$
Multiply by $\frac{10}{10}$.
$\Rightarrow p(8)=\sqrt{\frac{7}{40}}\cdot \sqrt{\frac{10}{10}}$
Use product property of square roots.
$\Rightarrow p(8)=\sqrt{\frac{7\cdot 10}{40\cdot 10}}$
Simplify.
$\Rightarrow p(8)=\sqrt{\frac{70}{400}}$
Use quotient property of square roots.
$\Rightarrow p(8)=\frac{\sqrt{70}}{\sqrt{400}}$
Simplify.
$\Rightarrow p(8)=\frac{\sqrt{70}}{20}$
Rounded to the nearest hundredth.
$\Rightarrow p(8)\approx 0.42$
