Question
Answer
$$-6^3\sqrt{28}-1^2\sqrt{175}^2=-216\cdot2\sqrt{7}-175$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-6^3\sqrt{28}-1^2\sqrt{175}^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-6^3\cdot2\sqrt{7}-1^2(5\sqrt{7})^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-216\cdot2\sqrt{7}-1\cdot175 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-216\cdot2\sqrt{7}-175\end{aligned} $$ | |
| ① | $$ \sqrt{175} =
\sqrt{ 5 ^2 \cdot 7 } =
\sqrt{ 5 ^2 } \, \sqrt{ 7 } =
5 \sqrt{ 7 }$$ |
| ② | $ 1 ^ 2 = 1 $$$ (5\sqrt{7})^2 =
5^{ 2 } \cdot \sqrt{7} ^ { 2 } =
5^{ 2 } \sqrt{7} ^2 =
5^{ 2 } \lvert 7 \rvert =
175 $$ |
| ③ | $ 1 \cdot 175 = 175 $ |
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