Question
Answer
$$(5\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})=22+4\sqrt{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}25+5\sqrt{15}-\sqrt{15}-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}22+4\sqrt{15}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( 5 \sqrt{5}- \sqrt{3}\right) } \cdot \left( \sqrt{5} + \sqrt{3}\right) = \color{blue}{ 5 \sqrt{5}} \cdot \sqrt{5}+\color{blue}{ 5 \sqrt{5}} \cdot \sqrt{3}\color{blue}{- \sqrt{3}} \cdot \sqrt{5}\color{blue}{- \sqrt{3}} \cdot \sqrt{3} = \\ = 25 + 5 \sqrt{15}- \sqrt{15}-3 $$ |
| ② | Combine like terms |
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