Perform. $\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }$ Express answers in simplest radical form.
A) $\sqrt [ 4 ] { 64 }$
B) $\sqrt [ 4 ] { 512 }$
C) $\sqrt [ 3 ] { 8 }$
D) $\sqrt [ 4 ] { 8 }$

Question

Quizplus · Accepted Answer

First, simplify the numerator: 
$$\sqrt [ 4 ] { 512 } = \sqrt [ 4 ]{2^9} = 2^{\frac{9}{4}}$$
Then simplify the denominator: $$\sqrt{8} = \sqrt{2\cdot 2\cdot 2} = 2\sqrt{2}$$
So the entire expression becomes: 
$$\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } } = \frac{2^{\frac{9}{4}}}{2\sqrt{2}} = 2^{\frac{1}{4}}\cdot 2^{\frac{5}{4}} \cdot \frac{1}{2\sqrt{2}} = \sqrt[4]{8} \cdot \frac{1}{2\sqrt{2}} = \frac{\sqrt[4]{8}}{2\sqrt{2}} = \boxed{\textbf{(D)}}$$

Perform 51248\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }8​4512​​

Perform $\frac { \sqrt [ 4 ] { 512 } } { \sqrt { 8 } }$