Question
Answer
$$\dfrac{4+\sqrt{2}+4-\sqrt{2}}{\sqrt{7}}=\dfrac{8\sqrt{7}}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4+\sqrt{2}+4-\sqrt{2}}{\sqrt{7}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{4+\sqrt{2}+4-\sqrt{2}}{1}}{\sqrt{7}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8}{\sqrt{7}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 8 }{\sqrt{ 7 }} \times \frac{ \color{orangered}{\sqrt{ 7 }} }{ \color{orangered}{\sqrt{ 7 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{8\sqrt{7}}{7}\end{aligned} $$ | |
| ① | $$ 4+\sqrt{2}+4-\sqrt{2}
= 4+\sqrt{2} \cdot \color{blue}{\frac{ 1 }{ 1}} + 4-\sqrt{2} \cdot \color{blue}{\frac{ 1 }{ 1}}
= \frac{4+\sqrt{2}+4-\sqrt{2}}{1} $$ |
| ② | Remove 1 from denominator. |
| ③ | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 7 }}$. |
| ④ | In denominator we have $ \sqrt{ 7 } \cdot \sqrt{ 7 } = 7 $. |
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