Rationalize the denominator and simplify the expression $343\frac { 3 } { \sqrt [ 3 ] { 4 } }$ .

A) $3234\frac { 3 \sqrt [ 3 ] { 2 } } { 4 }$
B) $\sqrt [ 3 ] { 4 }$
C) $3232\frac { 3 \sqrt [ 3 ] { 2 } } { 2 }$
D) $322\frac { 3 \sqrt { 2 } } { 2 }$
E) $2323\frac { 2 } { 3 \sqrt [ 3 ] { 2 } }$

Question

Rationalize the denominator and simplify the expression

343\frac { 3 } { \sqrt [ 3 ] { 4 } }

.

A)

3234\frac { 3 \sqrt [ 3 ] { 2 } } { 4 }

B)

\sqrt [ 3 ] { 4 }

C)

3232\frac { 3 \sqrt [ 3 ] { 2 } } { 2 }

D)

322\frac { 3 \sqrt { 2 } } { 2 }

E)

2323\frac { 2 } { 3 \sqrt [ 3 ] { 2 } }

myself Zubair · Accepted Answer

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

Rationalize the denominator and simplify the expression $343\frac { 3 } { \sqrt [ 3 ] { 4 } }$ .

A) $3234\frac { 3 \sqrt [ 3 ] { 2 } } { 4 }$
B) $\sqrt [ 3 ] { 4 }$
C) $3232\frac { 3 \sqrt [ 3 ] { 2 } } { 2 }$
D) $322\frac { 3 \sqrt { 2 } } { 2 }$
E) $2323\frac { 2 } { 3 \sqrt [ 3 ] { 2 } }$

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