Question
Answer
$$5\sqrt{8}-3\sqrt{18}+\sqrt{3}=\sqrt{2}+\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\sqrt{8}-3\sqrt{18}+\sqrt{3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}10\sqrt{2}-9\sqrt{2}+\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\sqrt{2}+\sqrt{3}\end{aligned} $$ | |
| ① | $$ 5 \sqrt{8} =
5 \sqrt{ 2 ^2 \cdot 2 } =
5 \sqrt{ 2 ^2 } \, \sqrt{ 2 } =
5 \cdot 2 \sqrt{ 2 } =
10 \sqrt{ 2 } $$ |
| ② | $$ - 3 \sqrt{18} =
-3 \sqrt{ 3 ^2 \cdot 2 } =
-3 \sqrt{ 3 ^2 } \, \sqrt{ 2 } =
-3 \cdot 3 \sqrt{ 2 } =
-9 \sqrt{ 2 } $$ |
| ③ | Combine like terms |
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