Question
Answer
$$7.071(\sqrt{3}+1)+7.071(\sqrt{3}-1)=14\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7.071(\sqrt{3}+1)+7.071(\sqrt{3}-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}7\sqrt{3}+7+7\sqrt{3}-7 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7\sqrt{3}+7+7\sqrt{3}-7}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}14\sqrt{3}\end{aligned} $$ | |
| ① | $$ \color{blue}{ 7 } \cdot \left( \sqrt{3} + 1\right) = \color{blue}{7} \cdot \sqrt{3}+\color{blue}{7} \cdot1 = \\ = 7 \sqrt{3} + 7 $$$$ \color{blue}{ 7 } \cdot \left( \sqrt{3}-1\right) = \color{blue}{7} \cdot \sqrt{3}+\color{blue}{7} \cdot-1 = \\ = 7 \sqrt{3}-7 $$ |
| ② | $$ 7\sqrt{3}+7+7\sqrt{3}-7
= 7\sqrt{3}+7 \cdot \color{blue}{\frac{ 1 }{ 1}} + 7\sqrt{3}-7 \cdot \color{blue}{\frac{ 1 }{ 1}}
= \frac{7\sqrt{3}+7+7\sqrt{3}-7}{1} $$ |
| ③ | Remove 1 from denominator. |
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