Question
Answer
$$\sqrt{44}+\sqrt{88}+\sqrt{99}+\sqrt{198}=5\sqrt{11}+5\sqrt{22}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{44}+\sqrt{88}+\sqrt{99}+\sqrt{198}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2\sqrt{11}+2\sqrt{22}+3\sqrt{11}+3\sqrt{22} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}5\sqrt{11}+5\sqrt{22}\end{aligned} $$ | |
| ① | $$ \sqrt{44} =
\sqrt{ 2 ^2 \cdot 11 } =
\sqrt{ 2 ^2 } \, \sqrt{ 11 } =
2 \sqrt{ 11 }$$ |
| ② | $$ \sqrt{88} =
\sqrt{ 2 ^2 \cdot 22 } =
\sqrt{ 2 ^2 } \, \sqrt{ 22 } =
2 \sqrt{ 22 }$$ |
| ③ | $$ \sqrt{99} =
\sqrt{ 3 ^2 \cdot 11 } =
\sqrt{ 3 ^2 } \, \sqrt{ 11 } =
3 \sqrt{ 11 }$$ |
| ④ | $$ \sqrt{198} =
\sqrt{ 3 ^2 \cdot 22 } =
\sqrt{ 3 ^2 } \, \sqrt{ 22 } =
3 \sqrt{ 22 }$$ |
| ⑤ | Combine like terms |
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