Question
Answer
$$\dfrac{4\sqrt{20}-\sqrt{72}}{3\sqrt{48}+2\sqrt{24}}=\dfrac{12\sqrt{15}-4\sqrt{30}-9\sqrt{6}+6\sqrt{3}}{42}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{20}-\sqrt{72}}{3\sqrt{48}+2\sqrt{24}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{20}-\sqrt{72}}{3\sqrt{48}+2\sqrt{24}}\frac{3\sqrt{48}-2\sqrt{24}}{3\sqrt{48}-2\sqrt{24}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{96\sqrt{15}-32\sqrt{30}-72\sqrt{6}+48\sqrt{3}}{432-144\sqrt{2}+144\sqrt{2}-96} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{96\sqrt{15}-32\sqrt{30}-72\sqrt{6}+48\sqrt{3}}{336} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{12\sqrt{15}-4\sqrt{30}-9\sqrt{6}+6\sqrt{3}}{42}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 3 \sqrt{48}- 2 \sqrt{24}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 4 \sqrt{20}- \sqrt{72}\right) } \cdot \left( 3 \sqrt{48}- 2 \sqrt{24}\right) = \color{blue}{ 4 \sqrt{20}} \cdot 3 \sqrt{48}+\color{blue}{ 4 \sqrt{20}} \cdot- 2 \sqrt{24}\color{blue}{- \sqrt{72}} \cdot 3 \sqrt{48}\color{blue}{- \sqrt{72}} \cdot- 2 \sqrt{24} = \\ = 96 \sqrt{15}- 32 \sqrt{30}- 72 \sqrt{6} + 48 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \left( 3 \sqrt{48} + 2 \sqrt{24}\right) } \cdot \left( 3 \sqrt{48}- 2 \sqrt{24}\right) = \color{blue}{ 3 \sqrt{48}} \cdot 3 \sqrt{48}+\color{blue}{ 3 \sqrt{48}} \cdot- 2 \sqrt{24}+\color{blue}{ 2 \sqrt{24}} \cdot 3 \sqrt{48}+\color{blue}{ 2 \sqrt{24}} \cdot- 2 \sqrt{24} = \\ = 432- 144 \sqrt{2} + 144 \sqrt{2}-96 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 8. |
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