Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers.
-$\frac { 9 } { \sqrt { 22 } }$
A) $\frac { 81 \sqrt { 22 } } { 22 }$
B) 493
C) $9 \sqrt { 22 }$
D) $\frac { 9 \sqrt { 22 } } { 22 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, we need to multiply both the numerator and denominator by the radical's conjugate. The conjugate of $\sqrt{22}$ is also $\sqrt{22}$ since the rational portion is 1. We then get: $$\frac{9}{\sqrt{22}}\cdot\frac{\sqrt{22}}{\sqrt{22}}=\frac{9\sqrt{22}}{22}$$This is simplest form since the numerator and denominator have no common factors greater than 1. Therefore, the answer is D.

Rationalize the Denominator and Simplify 922\frac { 9 } { \sqrt { 22 } }22​9​

Rationalize the Denominator and Simplify $\frac { 9 } { \sqrt { 22 } }$