Question
Answer
$$-8\sqrt{63}+\sqrt{112}=-20\sqrt{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-8\sqrt{63}+\sqrt{112}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-24\sqrt{7}+4\sqrt{7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-20\sqrt{7}\end{aligned} $$ | |
| ① | $$ - 8 \sqrt{63} =
-8 \sqrt{ 3 ^2 \cdot 7 } =
-8 \sqrt{ 3 ^2 } \, \sqrt{ 7 } =
-8 \cdot 3 \sqrt{ 7 } =
-24 \sqrt{ 7 } $$ |
| ② | $$ \sqrt{112} =
\sqrt{ 4 ^2 \cdot 7 } =
\sqrt{ 4 ^2 } \, \sqrt{ 7 } =
4 \sqrt{ 7 }$$ |
| ③ | Combine like terms |
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