Question
Answer
$$\sqrt{28}^2-4\sqrt{63}^4=-15848$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{28}^2-4\sqrt{63}^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2\sqrt{7})^2-4(3\sqrt{7})^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}28-4\cdot3969 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-15848\end{aligned} $$ | |
| ① | $$ \sqrt{28} =
\sqrt{ 2 ^2 \cdot 7 } =
\sqrt{ 2 ^2 } \, \sqrt{ 7 } =
2 \sqrt{ 7 }$$ |
| ② | $$ \sqrt{63} =
\sqrt{ 3 ^2 \cdot 7 } =
\sqrt{ 3 ^2 } \, \sqrt{ 7 } =
3 \sqrt{ 7 }$$ |
| ③ | $$ (2\sqrt{7})^2 =
2^{ 2 } \cdot \sqrt{7} ^ { 2 } =
2^{ 2 } \sqrt{7} ^2 =
2^{ 2 } \lvert 7 \rvert =
28 $$$$ (3\sqrt{7})^4 =
3^{ 4 } \cdot \sqrt{7} ^ { 4 } =
3^{ 4 } \left( \sqrt{7} ^2 \right)^{ 2 } =
3^{ 4 } \lvert 7 \rvert ^{ 2 } =
3969 $$ |
| ④ | Combine like terms |
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