Question
Answer
$$\dfrac{2+3\sqrt{8}}{\sqrt{10}}=\dfrac{\sqrt{10}+6\sqrt{5}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2+3\sqrt{8}}{\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2+3\sqrt{8}}{\sqrt{10}}\frac{\sqrt{10}}{\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2\sqrt{10}+12\sqrt{5}}{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{10}+6\sqrt{5}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 2 + 3 \sqrt{8}\right) } \cdot \sqrt{10} = \color{blue}{2} \cdot \sqrt{10}+\color{blue}{ 3 \sqrt{8}} \cdot \sqrt{10} = \\ = 2 \sqrt{10} + 12 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \sqrt{10} } \cdot \sqrt{10} = 10 $$ |
| ③ | Divide both numerator and denominator by 2. |
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