Answer
$$\sqrt{8}\cdot(\sqrt{13}-4\sqrt{117})=-22\sqrt{26}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{8}\cdot(\sqrt{13}-4\sqrt{117})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2\sqrt{2}(\sqrt{13}-12\sqrt{13}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2\sqrt{2}\cdot-11\sqrt{13} \xlongequal{ } \\[1 em] & \xlongequal{ }2\cdot(-11)\sqrt{2\cdot13} \xlongequal{ } \\[1 em] & \xlongequal{ }-22\sqrt{26}\end{aligned} $$ | |
| ① | $$ \sqrt{8} =
\sqrt{ 2 ^2 \cdot 2 } =
\sqrt{ 2 ^2 } \, \sqrt{ 2 } =
2 \sqrt{ 2 }$$ |
| ② | $$ - 4 \sqrt{117} =
-4 \sqrt{ 3 ^2 \cdot 13 } =
-4 \sqrt{ 3 ^2 } \, \sqrt{ 13 } =
-4 \cdot 3 \sqrt{ 13 } =
-12 \sqrt{ 13 } $$ |
| ③ | Combine like terms |
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