Question
Answer
$$\sqrt{2}\cdot(\sqrt{45}+\sqrt{5})=4\sqrt{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{2}\cdot(\sqrt{45}+\sqrt{5})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\sqrt{2}\cdot(3\sqrt{5}+\sqrt{5}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\sqrt{2}\cdot4\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ }4\sqrt{2\cdot5} \xlongequal{ } \\[1 em] & \xlongequal{ }4\sqrt{10}\end{aligned} $$ | |
| ① | $$ \sqrt{45} =
\sqrt{ 3 ^2 \cdot 5 } =
\sqrt{ 3 ^2 } \, \sqrt{ 5 } =
3 \sqrt{ 5 }$$ |
| ② | Combine like terms |
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