Question
Answer
$$\dfrac{20}{5\sqrt{7}-2\sqrt{5}}=\dfrac{100\sqrt{7}+40\sqrt{5}}{155}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{20}{5\sqrt{7}-2\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{20}{5\sqrt{7}-2\sqrt{5}}\frac{5\sqrt{7}+2\sqrt{5}}{5\sqrt{7}+2\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{100\sqrt{7}+40\sqrt{5}}{175+10\sqrt{35}-10\sqrt{35}-20} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{100\sqrt{7}+40\sqrt{5}}{155}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5 \sqrt{7} + 2 \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 20 } \cdot \left( 5 \sqrt{7} + 2 \sqrt{5}\right) = \color{blue}{20} \cdot 5 \sqrt{7}+\color{blue}{20} \cdot 2 \sqrt{5} = \\ = 100 \sqrt{7} + 40 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \left( 5 \sqrt{7}- 2 \sqrt{5}\right) } \cdot \left( 5 \sqrt{7} + 2 \sqrt{5}\right) = \color{blue}{ 5 \sqrt{7}} \cdot 5 \sqrt{7}+\color{blue}{ 5 \sqrt{7}} \cdot 2 \sqrt{5}\color{blue}{- 2 \sqrt{5}} \cdot 5 \sqrt{7}\color{blue}{- 2 \sqrt{5}} \cdot 2 \sqrt{5} = \\ = 175 + 10 \sqrt{35}- 10 \sqrt{35}-20 $$ |
| ③ | Simplify numerator and denominator |
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