Answer
$\sqrt{\dfrac{8x^{5}y}{2z}}=\dfrac{2x^{3}y}{\sqrt{xyz}}$
Work Step by Step
$\sqrt{\dfrac{8x^{5}y}{2z}}$
Rewrite this expression as $\dfrac{\sqrt{4\cdot2(x^{5}y)}}{\sqrt{2z}}$ and simplify it:
$\sqrt{\dfrac{8x^{5}y}{2z}}=\dfrac{\sqrt{4\cdot2(x^{5}y)}}{\sqrt{2z}}=\dfrac{2x^{2}\sqrt{2xy}}{\sqrt{2z}}=...$
Multiply the fraction by $\dfrac{\sqrt{2xy}}{\sqrt{2xy}}$ and simplify again if possible:
$...=\dfrac{2x^{2}\sqrt{2xy}}{\sqrt{2z}}\cdot\dfrac{\sqrt{2xy}}{\sqrt{2xy}}=\dfrac{2x^{2}\sqrt{(2xy)^{2}}}{\sqrt{4xyz}}=\dfrac{2x^{2}(2xy)}{2\sqrt{xyz}}=...$
$...=\dfrac{2x^{3}y}{\sqrt{xyz}}$
