Question
Answer
$$\dfrac{\sqrt{50}+\sqrt{48}}{\sqrt{98}+\sqrt{8}}=\dfrac{5+2\sqrt{6}}{9}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{50}+\sqrt{48}}{\sqrt{98}+\sqrt{8}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{50}+\sqrt{48}}{\sqrt{98}+\sqrt{8}}\frac{\sqrt{98}-\sqrt{8}}{\sqrt{98}-\sqrt{8}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{70-20+28\sqrt{6}-8\sqrt{6}}{98-28+28-8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{50+20\sqrt{6}}{90} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5+2\sqrt{6}}{9}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{98}- \sqrt{8}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{50} + \sqrt{48}\right) } \cdot \left( \sqrt{98}- \sqrt{8}\right) = \color{blue}{ \sqrt{50}} \cdot \sqrt{98}+\color{blue}{ \sqrt{50}} \cdot- \sqrt{8}+\color{blue}{ \sqrt{48}} \cdot \sqrt{98}+\color{blue}{ \sqrt{48}} \cdot- \sqrt{8} = \\ = 70-20 + 28 \sqrt{6}- 8 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{98} + \sqrt{8}\right) } \cdot \left( \sqrt{98}- \sqrt{8}\right) = \color{blue}{ \sqrt{98}} \cdot \sqrt{98}+\color{blue}{ \sqrt{98}} \cdot- \sqrt{8}+\color{blue}{ \sqrt{8}} \cdot \sqrt{98}+\color{blue}{ \sqrt{8}} \cdot- \sqrt{8} = \\ = 98-28 + 28-8 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 10. |
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