Simplify the expression.Assume that all variables represent positive numbers, so that no absolute value symbols are needed. $$\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }$$
A) $\quad 12 y \sqrt { 2 x y }$
B) $\quad 8 y \sqrt { 3 x y }$
C) $\quad 4 y \sqrt { 2 x y }$
D) $\quad 4 y \sqrt { 4 x y }$

Question

Quizplus · Accepted Answer

First, notice that the first and third terms cancel each other out. We are left with:
$$y\sqrt[4]{512xy}=y\sqrt[4]{2^9xy}=y\cdot2\sqrt[4]{2xy}=4y\sqrt{2xy}$$
Thus, the answer is $\boxed{\textbf{(C)}\ 4y\sqrt{2xy}}$.

Simplify the Expression 2xy54+y512xy4−2xy54\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }42xy5​+y4512xy​−42xy5​

Simplify the Expression $\sqrt [ 4 ] { 2 x y ^ { 5 } } + y \sqrt [ 4 ] { 512 x y } - \sqrt [ 4 ] { 2 x y ^ { 5 } }$