Question
Answer
$$\sqrt{8}\cdot(\sqrt{2}-7)=4-14\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{8}\cdot(\sqrt{2}-7)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2\sqrt{2}(\sqrt{2}-7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4-14\sqrt{2}\end{aligned} $$ | |
| ① | $$ \sqrt{8} =
\sqrt{ 2 ^2 \cdot 2 } =
\sqrt{ 2 ^2 } \, \sqrt{ 2 } =
2 \sqrt{ 2 }$$ |
| ② | $$ \color{blue}{ 2 \sqrt{2} } \cdot \left( \sqrt{2}-7\right) = \color{blue}{ 2 \sqrt{2}} \cdot \sqrt{2}+\color{blue}{ 2 \sqrt{2}} \cdot-7 = \\ = 4- 14 \sqrt{2} $$ |
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