Answer
$$\frac{30}{\sqrt{20}-\sqrt{5}}=6\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{30}{\sqrt{20}-\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{30}{\sqrt{20}-\sqrt{5}}\frac{\sqrt{20}+\sqrt{5}}{\sqrt{20}+\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{60\sqrt{5}+30\sqrt{5}}{20+10-10-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{90\sqrt{5}}{15} \xlongequal{ } \\[1 em] & \xlongequal{ }6\sqrt{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{20} + \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 30 } \cdot \left( \sqrt{20} + \sqrt{5}\right) = \color{blue}{30} \cdot \sqrt{20}+\color{blue}{30} \cdot \sqrt{5} = \\ = 60 \sqrt{5} + 30 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{20}- \sqrt{5}\right) } \cdot \left( \sqrt{20} + \sqrt{5}\right) = \color{blue}{ \sqrt{20}} \cdot \sqrt{20}+\color{blue}{ \sqrt{20}} \cdot \sqrt{5}\color{blue}{- \sqrt{5}} \cdot \sqrt{20}\color{blue}{- \sqrt{5}} \cdot \sqrt{5} = \\ = 20 + 10-10-5 $$ |
| ③ | Simplify numerator and denominator |
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