Rationalize the denominator and simplify. All variables represent positive real numbers. $\frac { \sqrt { 3 } } { \sqrt { 11 } - \sqrt { 7 } }$
A) $\frac { \sqrt { 33 } - \sqrt { 21 } } { 4 }$
B) $\frac { \sqrt { 33 } + \sqrt { 21 } } { 18 }$
C) $\frac { \sqrt { 33 } + \sqrt { 21 } } { 4 }$
D) $\frac { \sqrt { 54 } } { 4 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, we need to multiply the numerator and denominator by the conjugate of the denominator, which is $\sqrt{11}+\sqrt{7}$. This gives us: $$\frac{\sqrt{3}(\sqrt{11}+\sqrt{7})}{(\sqrt{11}-\sqrt{7})(\sqrt{11}+\sqrt{7})}=\frac{\sqrt{33}+\sqrt{21}}{11-7}=\frac{\sqrt{33}+\sqrt{21}}{4}$$

Rationalize the Denominator and Simplify 311−7\frac { \sqrt { 3 } } { \sqrt { 11 } - \sqrt { 7 } }11​−7​3​​

Rationalize the Denominator and Simplify $\frac { \sqrt { 3 } } { \sqrt { 11 } - \sqrt { 7 } }$