Answer
$$\frac{22}{6+\sqrt{24}}=\frac{132-44\sqrt{6}}{12}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{22}{6+\sqrt{24}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{22}{6+\sqrt{24}}\frac{6-\sqrt{24}}{6-\sqrt{24}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{132-44\sqrt{6}}{36-12\sqrt{6}+12\sqrt{6}-24} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{132-44\sqrt{6}}{12}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 6- \sqrt{24}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 22 } \cdot \left( 6- \sqrt{24}\right) = \color{blue}{22} \cdot6+\color{blue}{22} \cdot- \sqrt{24} = \\ = 132- 44 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( 6 + \sqrt{24}\right) } \cdot \left( 6- \sqrt{24}\right) = \color{blue}{6} \cdot6+\color{blue}{6} \cdot- \sqrt{24}+\color{blue}{ \sqrt{24}} \cdot6+\color{blue}{ \sqrt{24}} \cdot- \sqrt{24} = \\ = 36- 12 \sqrt{6} + 12 \sqrt{6}-24 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator