Question
Answer
$$\dfrac{40\cdot(3+\sqrt{3})}{\sqrt{3}}=\dfrac{120\sqrt{3}+120}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{40\cdot(3+\sqrt{3})}{\sqrt{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{120+40\sqrt{3}}{\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{120+40\sqrt{3}}{\sqrt{3}}\frac{\sqrt{3}}{\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{120\sqrt{3}+120}{3}\end{aligned} $$ | |
| ① | $$ \color{blue}{ 40 } \cdot \left( 3 + \sqrt{3}\right) = \color{blue}{40} \cdot3+\color{blue}{40} \cdot \sqrt{3} = \\ = 120 + 40 \sqrt{3} $$ |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ \left( 120 + 40 \sqrt{3}\right) } \cdot \sqrt{3} = \color{blue}{120} \cdot \sqrt{3}+\color{blue}{ 40 \sqrt{3}} \cdot \sqrt{3} = \\ = 120 \sqrt{3} + 120 $$ Simplify denominator. $$ \color{blue}{ \sqrt{3} } \cdot \sqrt{3} = 3 $$ |
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