Question
Answer
$$\dfrac{4\sqrt{80}+\sqrt{112}}{4\sqrt{20}}=\dfrac{20+\sqrt{35}}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{80}+\sqrt{112}}{4\sqrt{20}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{80}+\sqrt{112}}{4\sqrt{20}}\frac{\sqrt{20}}{\sqrt{20}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{160+8\sqrt{35}}{80} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{20+\sqrt{35}}{10}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{20}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 4 \sqrt{80} + \sqrt{112}\right) } \cdot \sqrt{20} = \color{blue}{ 4 \sqrt{80}} \cdot \sqrt{20}+\color{blue}{ \sqrt{112}} \cdot \sqrt{20} = \\ = 160 + 8 \sqrt{35} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{20} } \cdot \sqrt{20} = 80 $$ |
| ③ | Divide both numerator and denominator by 8. |
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