Question
Answer
$$(-5-3\sqrt{7})\cdot(4-\sqrt{7})=1-7\sqrt{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-5-3\sqrt{7})\cdot(4-\sqrt{7})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-20+5\sqrt{7}-12\sqrt{7}+21 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}1-7\sqrt{7}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( -5- 3 \sqrt{7}\right) } \cdot \left( 4- \sqrt{7}\right) = \color{blue}{-5} \cdot4\color{blue}{-5} \cdot- \sqrt{7}\color{blue}{- 3 \sqrt{7}} \cdot4\color{blue}{- 3 \sqrt{7}} \cdot- \sqrt{7} = \\ = -20 + 5 \sqrt{7}- 12 \sqrt{7} + 21 $$ |
| ② | Combine like terms |
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