Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$\sqrt [ 4 ] { 486 }$
A) 22
B) $6 \sqrt [ 4 ] { 3 }$
C) $3 \sqrt [ 4 ] { 6 }$
D) 4

Question

Quizplus · Accepted Answer

We can simplify this expression by factoring 486 into primes and using the property that $\sqrt [ n ] { a \cdot b } = \sqrt [ n ] { a } \cdot \sqrt [ n ] { b }$. 
First, note that 486 is divisible by 2. 
\begin{align*}
\sqrt [ 4 ] { 486 } &= \sqrt [ 4 ] { 2^2 \cdot 3^5 } \
&= \sqrt [ 4 ] { 2^2 } \cdot \sqrt [ 4 ] { 3^5 } \
&= 2^{2/4} \cdot 3^{5/4} \
&= 2 \cdot \sqrt [ 4 ] { 3^5 } \
&= 2 \cdot \sqrt [ 4 ] { 3^4 \cdot 3 } \
&= 2 \cdot 3 \sqrt [ 4 ] { 3 } \
&= 6 \sqrt [ 4 ] { 3 }
\end{align*}
Therefore, the answer is choice C.

Write the Word or Phrase That Best Completes Each Statement 4864\sqrt [ 4 ] { 486 }4486​

Write the Word or Phrase That Best Completes Each Statement $\sqrt [ 4 ] { 486 }$