Question
Answer
$$\dfrac{\sqrt{3}}{2\sqrt{15}-\sqrt{2}}=\dfrac{6\sqrt{5}+\sqrt{6}}{58}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{3}}{2\sqrt{15}-\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{3}}{2\sqrt{15}-\sqrt{2}}\frac{2\sqrt{15}+\sqrt{2}}{2\sqrt{15}+\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{5}+\sqrt{6}}{60+2\sqrt{30}-2\sqrt{30}-2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6\sqrt{5}+\sqrt{6}}{58}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 2 \sqrt{15} + \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{3} } \cdot \left( 2 \sqrt{15} + \sqrt{2}\right) = \color{blue}{ \sqrt{3}} \cdot 2 \sqrt{15}+\color{blue}{ \sqrt{3}} \cdot \sqrt{2} = \\ = 6 \sqrt{5} + \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( 2 \sqrt{15}- \sqrt{2}\right) } \cdot \left( 2 \sqrt{15} + \sqrt{2}\right) = \color{blue}{ 2 \sqrt{15}} \cdot 2 \sqrt{15}+\color{blue}{ 2 \sqrt{15}} \cdot \sqrt{2}\color{blue}{- \sqrt{2}} \cdot 2 \sqrt{15}\color{blue}{- \sqrt{2}} \cdot \sqrt{2} = \\ = 60 + 2 \sqrt{30}- 2 \sqrt{30}-2 $$ |
| ③ | Simplify numerator and denominator |
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