Answer
$r(4)=\frac{\sqrt{2}}{3}$
$r(4)\approx 0.47$
Work Step by Step
The given function is
$\Rightarrow r(x)=\sqrt{\frac{3x}{3x^2+6}}$
Substitute $4$ for $x$.
$\Rightarrow r(4)=\sqrt{\frac{3(4)}{3(4)^2+6}}$
Simplify.
$\Rightarrow r(4)=\sqrt{\frac{12}{3(16)+6}}$
Factor as square term.
$\Rightarrow r(4)=\sqrt{\frac{12}{48+6}}$
$\Rightarrow r(4)=\sqrt{\frac{12}{54}}$
Simplify.
$\Rightarrow r(4)=\sqrt{\frac{2}{9}}$
Use quotient property of square roots.
$\Rightarrow r(4)=\frac{\sqrt{2}}{\sqrt{9}}$
Simplify.
$\Rightarrow r(4)=\frac{\sqrt{2}}{3}$
Rounded to the nearest hundredth.
$\Rightarrow r(4)\approx 0.47$
