Question
Answer
$$6\sqrt{175}-7\sqrt{28}+\sqrt{56}=16\sqrt{7}+2\sqrt{14}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6\sqrt{175}-7\sqrt{28}+\sqrt{56}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}30\sqrt{7}-14\sqrt{7}+2\sqrt{14} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}16\sqrt{7}+2\sqrt{14}\end{aligned} $$ | |
| ① | $$ 6 \sqrt{175} =
6 \sqrt{ 5 ^2 \cdot 7 } =
6 \sqrt{ 5 ^2 } \, \sqrt{ 7 } =
6 \cdot 5 \sqrt{ 7 } =
30 \sqrt{ 7 } $$ |
| ② | $$ - 7 \sqrt{28} =
-7 \sqrt{ 2 ^2 \cdot 7 } =
-7 \sqrt{ 2 ^2 } \, \sqrt{ 7 } =
-7 \cdot 2 \sqrt{ 7 } =
-14 \sqrt{ 7 } $$ |
| ③ | $$ \sqrt{56} =
\sqrt{ 2 ^2 \cdot 14 } =
\sqrt{ 2 ^2 } \, \sqrt{ 14 } =
2 \sqrt{ 14 }$$ |
| ④ | Combine like terms |
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