Question
Answer
$$\dfrac{3\sqrt{6}+4}{2\sqrt{6}}=\dfrac{9+2\sqrt{6}}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{6}+4}{2\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{6}+4}{2\sqrt{6}}\frac{\sqrt{6}}{\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{18+4\sqrt{6}}{12} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{9+2\sqrt{6}}{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 3 \sqrt{6} + 4\right) } \cdot \sqrt{6} = \color{blue}{ 3 \sqrt{6}} \cdot \sqrt{6}+\color{blue}{4} \cdot \sqrt{6} = \\ = 18 + 4 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{6} } \cdot \sqrt{6} = 12 $$ |
| ③ | Divide both numerator and denominator by 2. |
This page was created using
Rationalize Denominator Calculator