Question
Answer
$$\dfrac{(6+\sqrt{3})\cdot(6-\sqrt{3})}{\sqrt{33}}=\sqrt{33}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(6+\sqrt{3})\cdot(6-\sqrt{3})}{\sqrt{33}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{36-6\sqrt{3}+6\sqrt{3}-3}{\sqrt{33}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{33}{\sqrt{33}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 33 }{\sqrt{ 33 }} \times \frac{ \color{orangered}{\sqrt{ 33 }} }{ \color{orangered}{\sqrt{ 33 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{33\sqrt{33}}{33} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}} \frac{ 33 \sqrt{ 33 } : \color{blue}{ 33 } }{ 33 : \color{blue}{ 33 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{33}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ }\sqrt{33}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( 6 + \sqrt{3}\right) } \cdot \left( 6- \sqrt{3}\right) = \color{blue}{6} \cdot6+\color{blue}{6} \cdot- \sqrt{3}+\color{blue}{ \sqrt{3}} \cdot6+\color{blue}{ \sqrt{3}} \cdot- \sqrt{3} = \\ = 36- 6 \sqrt{3} + 6 \sqrt{3}-3 $$ |
| ② | Simplify numerator and denominator |
| ③ | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 33 }}$. |
| ④ | In denominator we have $ \sqrt{ 33 } \cdot \sqrt{ 33 } = 33 $. |
| ⑤ | Divide both the top and bottom numbers by $ \color{blue}{ 33 }$. |
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