Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { \sqrt { 5 } } { \sqrt { 11 } + 2 }$
A) $\frac { \sqrt { 55 } + 2 \sqrt { 5 } } { 7 }$
B) $\frac { 3 \sqrt { 55 } + 115 } { 22 }$
C) $\frac { \sqrt { 55 } - 2 \sqrt { 5 } } { 7 }$
D) $\frac { \sqrt { 55 } - 2 \sqrt { 5 } } { 13 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator: $\sqrt{11} - 2$. This results in $\frac{\sqrt{5}(\sqrt{11} - 2)}{(\sqrt{11} + 2)(\sqrt{11} - 2)} = \frac{\sqrt{55} - 2\sqrt{5}}{11 - 4} = \frac{\sqrt{55} - 2\sqrt{5}}{7}$.

Rationalize the Denominator 511+2\frac { \sqrt { 5 } } { \sqrt { 11 } + 2 }11​+25​​

Rationalize the Denominator $\frac { \sqrt { 5 } } { \sqrt { 11 } + 2 }$