Question
Answer
$$\dfrac{4}{5\sqrt{2}+2}=\dfrac{20\sqrt{2}-8}{46}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4}{5\sqrt{2}+2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4}{5\sqrt{2}+2}\frac{5\sqrt{2}-2}{5\sqrt{2}-2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{20\sqrt{2}-8}{50-10\sqrt{2}+10\sqrt{2}-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{20\sqrt{2}-8}{46}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5 \sqrt{2}-2} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 } \cdot \left( 5 \sqrt{2}-2\right) = \color{blue}{4} \cdot 5 \sqrt{2}+\color{blue}{4} \cdot-2 = \\ = 20 \sqrt{2}-8 $$ Simplify denominator. $$ \color{blue}{ \left( 5 \sqrt{2} + 2\right) } \cdot \left( 5 \sqrt{2}-2\right) = \color{blue}{ 5 \sqrt{2}} \cdot 5 \sqrt{2}+\color{blue}{ 5 \sqrt{2}} \cdot-2+\color{blue}{2} \cdot 5 \sqrt{2}+\color{blue}{2} \cdot-2 = \\ = 50- 10 \sqrt{2} + 10 \sqrt{2}-4 $$ |
| ③ | Simplify numerator and denominator |
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