Answer
$$\frac{3-3\sqrt{3}}{4\sqrt{8}}=\frac{6\sqrt{2}-6\sqrt{6}}{32}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3-3\sqrt{3}}{4\sqrt{8}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3-3\sqrt{3}}{4\sqrt{8}}\frac{\sqrt{8}}{\sqrt{8}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{2}-6\sqrt{6}}{32}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{8}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 3- 3 \sqrt{3}\right) } \cdot \sqrt{8} = \color{blue}{3} \cdot \sqrt{8}\color{blue}{- 3 \sqrt{3}} \cdot \sqrt{8} = \\ = 6 \sqrt{2}- 6 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{8} } \cdot \sqrt{8} = 32 $$ |
This page was created using
Rationalize Denominator Calculator