Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { \sqrt { 2 } } { 2 \sqrt { 3 } - \sqrt { 2 } }$
A) $\frac { \sqrt { 6 } + 1 } { 5 }$
B) $\frac { \sqrt { 6 } + 1 } { 7 }$
C) $\frac { \sqrt { 3 } + 1 } { 5 }$
D) $\frac { \sqrt { 6 } - 1 } { 5 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { \sqrt { 2 } } { 2 \sqrt { 3 } - \sqrt { 2 } }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $2\sqrt{3} + \sqrt{2}$. This process eliminates the square roots in the denominator and simplifies to $\frac { \sqrt { 6 } + 1 } { 5 }$.

Rationalize the Denominator 223−2\frac { \sqrt { 2 } } { 2 \sqrt { 3 } - \sqrt { 2 } }23​−2​2​​

Rationalize the Denominator $\frac { \sqrt { 2 } } { 2 \sqrt { 3 } - \sqrt { 2 } }$