Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$$\frac { 3 } { 6 - \sqrt { 2 } }$$
A) $\frac { 18 + 3 \sqrt { 2 } } { 4 }$

B) $\frac { 3 } { 6 } - \frac { 3 } { \sqrt { 2 } }$

C) $\frac { 18 - 3 \sqrt { 2 } } { 34 }$

D) $\frac { 18 + 3 \sqrt { 2 } } { 34 }$

Question

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$$\frac { 3 } { 6 - \sqrt { 2 } }$$
A) $\frac { 18 + 3 \sqrt { 2 } } { 4 }$

B) $\frac { 3 } { 6 } - \frac { 3 } { \sqrt { 2 } }$

C) $\frac { 18 - 3 \sqrt { 2 } } { 34 }$

D) $\frac { 18 + 3 \sqrt { 2 } } { 34 }$

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator: $6 + \sqrt{2}$. This results in $\frac{3(6 + \sqrt{2})}{(6 - \sqrt{2})(6 + \sqrt{2})}$. Simplifying gives $\frac{18 + 3\sqrt{2}}{34}$.

Rationalize the Denominator 36−2\frac { 3 } { 6 - \sqrt { 2 } }6−2​3​

Rationalize the Denominator $\frac { 3 } { 6 - \sqrt { 2 } }$