Question
Answer
$$6\sqrt{126}+3\sqrt{126}+8\sqrt{126}=51\sqrt{14}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6\sqrt{126}+3\sqrt{126}+8\sqrt{126}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}18\sqrt{14}+9\sqrt{14}+24\sqrt{14} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}51\sqrt{14}\end{aligned} $$ | |
| ① | $$ 6 \sqrt{126} =
6 \sqrt{ 3 ^2 \cdot 14 } =
6 \sqrt{ 3 ^2 } \, \sqrt{ 14 } =
6 \cdot 3 \sqrt{ 14 } =
18 \sqrt{ 14 } $$ |
| ② | $$ 3 \sqrt{126} =
3 \sqrt{ 3 ^2 \cdot 14 } =
3 \sqrt{ 3 ^2 } \, \sqrt{ 14 } =
3 \cdot 3 \sqrt{ 14 } =
9 \sqrt{ 14 } $$ |
| ③ | $$ 8 \sqrt{126} =
8 \sqrt{ 3 ^2 \cdot 14 } =
8 \sqrt{ 3 ^2 } \, \sqrt{ 14 } =
8 \cdot 3 \sqrt{ 14 } =
24 \sqrt{ 14 } $$ |
| ④ | Combine like terms |
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