Answer
$$\frac{\sqrt{10}+\sqrt{15}}{\sqrt{5}}=\sqrt{2}+\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{10}+\sqrt{15}}{\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{10}+\sqrt{15}}{\sqrt{5}}\frac{\sqrt{5}}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5\sqrt{2}+5\sqrt{3}}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{2}+\sqrt{3}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\sqrt{2}+\sqrt{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{10} + \sqrt{15}\right) } \cdot \sqrt{5} = \color{blue}{ \sqrt{10}} \cdot \sqrt{5}+\color{blue}{ \sqrt{15}} \cdot \sqrt{5} = \\ = 5 \sqrt{2} + 5 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \sqrt{5} } \cdot \sqrt{5} = 5 $$ |
| ③ | Divide both numerator and denominator by 5. |
| ④ | Remove 1 from denominator. |
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