Question
Answer
$$7.071(\sqrt{3}-1)\cdot7.071(\sqrt{3}-1)=196-98\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7.071(\sqrt{3}-1)\cdot7.071(\sqrt{3}-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(7\sqrt{3}-7)(7\sqrt{3}-7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}147-49\sqrt{3}-49\sqrt{3}+49 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}196-98\sqrt{3}\end{aligned} $$ | |
| ① | $$ \color{blue}{ 7 } \cdot \left( \sqrt{3}-1\right) = \color{blue}{7} \cdot \sqrt{3}+\color{blue}{7} \cdot-1 = \\ = 7 \sqrt{3}-7 $$$$ \color{blue}{ 7 } \cdot \left( \sqrt{3}-1\right) = \color{blue}{7} \cdot \sqrt{3}+\color{blue}{7} \cdot-1 = \\ = 7 \sqrt{3}-7 $$ |
| ② | $$ \color{blue}{ \left( 7 \sqrt{3}-7\right) } \cdot \left( 7 \sqrt{3}-7\right) = \color{blue}{ 7 \sqrt{3}} \cdot 7 \sqrt{3}+\color{blue}{ 7 \sqrt{3}} \cdot-7\color{blue}{-7} \cdot 7 \sqrt{3}\color{blue}{-7} \cdot-7 = \\ = 147- 49 \sqrt{3}- 49 \sqrt{3} + 49 $$ |
| ③ | Combine like terms |
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