Question
Answer
$$\dfrac{5}{5\sqrt{20}+7}=\dfrac{50\sqrt{5}-35}{451}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{5\sqrt{20}+7}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{5\sqrt{20}+7}\frac{5\sqrt{20}-7}{5\sqrt{20}-7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{50\sqrt{5}-35}{500-70\sqrt{5}+70\sqrt{5}-49} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{50\sqrt{5}-35}{451}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5 \sqrt{20}-7} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( 5 \sqrt{20}-7\right) = \color{blue}{5} \cdot 5 \sqrt{20}+\color{blue}{5} \cdot-7 = \\ = 50 \sqrt{5}-35 $$ Simplify denominator. $$ \color{blue}{ \left( 5 \sqrt{20} + 7\right) } \cdot \left( 5 \sqrt{20}-7\right) = \color{blue}{ 5 \sqrt{20}} \cdot 5 \sqrt{20}+\color{blue}{ 5 \sqrt{20}} \cdot-7+\color{blue}{7} \cdot 5 \sqrt{20}+\color{blue}{7} \cdot-7 = \\ = 500- 70 \sqrt{5} + 70 \sqrt{5}-49 $$ |
| ③ | Simplify numerator and denominator |
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