Rationalize the denominator and simplify the expression $\frac { 3 } { \sqrt [ 3 ] { 4 } }$ .
A) $\frac { 3 \sqrt [ 3 ] { 2 } } { 4 }$
B) $3 \sqrt [ 3 ] { 4 }$
C) $\frac { 3 \sqrt [ 3 ] { 2 } } { 2 }$
D) $\frac { 3 \sqrt { 2 } } { 2 }$
E) $\frac { 2 } { 3 \sqrt [ 3 ] { 2 } }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { 3 } { \sqrt [ 3 ] { 4 } }$, multiply both the numerator and denominator by $\sqrt [ 3 ] { 2^2 }$ (which is $\sqrt [ 3 ] { 4 }$) to make the denominator a rational number. This results in $\frac { 3 \sqrt [ 3 ] { 4 } } { 4 }$, which simplifies to $\frac { 3 \sqrt [ 3 ] { 2^2 } } { 2^2 }$ or $\frac { 3 \sqrt [ 3 ] { 2 } } { 2 }$, since $4 = 2^2$ and $\sqrt [ 3 ] { 2^2 } = \sqrt [ 3 ] { 4 }$.

Rationalize the Denominator and Simplify the Expression 343\frac { 3 } { \sqrt [ 3 ] { 4 } }34​3​

Rationalize the Denominator and Simplify the Expression $\frac { 3 } { \sqrt [ 3 ] { 4 } }$