Answer
$\displaystyle \frac{2\sqrt{a^{2}+b^{2}}}{c}$
Work Step by Step
Simplify the radicand by finding as many squared factors as possible:
$4=2^{2}$
$\displaystyle \frac{1}{c^{2}}=(\frac{1}{c})^{2}$
$\sqrt{\dfrac{4(x^{2}+y^{2})}{c^{2}}}=\sqrt{2^{2}(\frac{1}{c})^{2}(a^{2}+b^{2})}$
... Radical of a product:
$=\sqrt{2^{2}}\cdot\sqrt{(\frac{1}{c})^{2}}\cdot\sqrt{a^{2}+b^{2}}$
... for even n, $\sqrt[n]{x^{n}}=|x|$,
... there is no formula to simplify the last factor,
$=|2|\displaystyle \cdot|\frac{1}{c}|\cdot\sqrt{a^{2}+b^{2}}$
... c is positive, so $|\displaystyle \frac{1}{c}|=\frac{1}{c}$
$=\displaystyle \frac{2\sqrt{a^{2}+b^{2}}}{c}$
