Answer
$$\frac{9-6\sqrt{2}}{\sqrt{30}}=\frac{3\sqrt{30}-4\sqrt{15}}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{9-6\sqrt{2}}{\sqrt{30}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{9-6\sqrt{2}}{\sqrt{30}}\frac{\sqrt{30}}{\sqrt{30}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{9\sqrt{30}-12\sqrt{15}}{30} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3\sqrt{30}-4\sqrt{15}}{10}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{30}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 9- 6 \sqrt{2}\right) } \cdot \sqrt{30} = \color{blue}{9} \cdot \sqrt{30}\color{blue}{- 6 \sqrt{2}} \cdot \sqrt{30} = \\ = 9 \sqrt{30}- 12 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ \sqrt{30} } \cdot \sqrt{30} = 30 $$ |
| ③ | Divide both numerator and denominator by 3. |
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