Rationalize Denominators
-$\frac { \sqrt { 6 } } { \sqrt { 17 } + 2 }$
A) $\frac { \sqrt { 102 } - 2 \sqrt { 6 } } { 13 }$
B) $\frac { \sqrt { 102 } + 2 \sqrt { 6 } } { 13 }$
C) $\frac { \sqrt { 102 } - 2 \sqrt { 6 } } { 19 }$
D) $\frac { 3 \sqrt { 102 } + 17 \sqrt { 34 } } { 6 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator $\frac { \sqrt { 6 } } { \sqrt { 17 } + 2 }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $\sqrt { 17 } - 2$. This results in $\frac { \sqrt { 6 }(\sqrt { 17 } - 2) } { (\sqrt { 17 } + 2)(\sqrt { 17 } - 2) }$. Simplifying the numerator gives $\sqrt { 102 } - 2\sqrt { 6 }$, and the denominator simplifies to $17 - 4 = 13$, resulting in $\frac { \sqrt { 102 } - 2 \sqrt { 6 } } { 13 }$.

Rationalize Denominators - 617+2\frac { \sqrt { 6 } } { \sqrt { 17 } + 2 }17​+26​​

Rationalize Denominators
- $\frac { \sqrt { 6 } } { \sqrt { 17 } + 2 }$