Question
Answer
$$\dfrac{\sqrt{3}+\sqrt{5}}{\sqrt{10}}=\dfrac{\sqrt{30}+5\sqrt{2}}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{3}+\sqrt{5}}{\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{3}+\sqrt{5}}{\sqrt{10}}\frac{\sqrt{10}}{\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\sqrt{30}+5\sqrt{2}}{10}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{3} + \sqrt{5}\right) } \cdot \sqrt{10} = \color{blue}{ \sqrt{3}} \cdot \sqrt{10}+\color{blue}{ \sqrt{5}} \cdot \sqrt{10} = \\ = \sqrt{30} + 5 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \sqrt{10} } \cdot \sqrt{10} = 10 $$ |
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