Perform the indicated operation and express your answer in simplest radical form. $\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }$ Express answers in simplest radical form.
A) $\sqrt [ 3 ] { 8 }$
B) $\sqrt [ 3 ] { 512 }$
C) $\sqrt [ 4 ] { 8 }$
D) $\sqrt [ 4 ] { 512 }$
E) $\sqrt [ 4 ] { 64 }$

Question

Quizplus · Accepted Answer

We can simplify $\sqrt{8}$ to $\sqrt{4}\cdot\sqrt{2}=2\sqrt{2}$. Then we simplify the expression as follows: 
$$\frac{\sqrt[4]{512}}{\sqrt{8}}=\frac{\sqrt[4]{2^9}}{2\sqrt{2}}=\frac{2\sqrt[4]{2^5}}{2\sqrt{2}}=\frac{2\cdot2\sqrt{2}}{2\sqrt{2}}=\boxed{2^\frac{3}{4}}$$
which is the same as $\sqrt[4]{8}$, or choice C.

Perform the Indicated Operation and Express Your Answer in Simplest 51248\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }8​4512​​

Perform the Indicated Operation and Express Your Answer in Simplest $\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }$