Answer
$$\frac{3\sqrt{2}+7\sqrt{5}}{2\sqrt{3}\cdot6\sqrt{5}}=\frac{3\sqrt{30}+35\sqrt{3}}{180}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{2}+7\sqrt{5}}{2\sqrt{3}\cdot6\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{2}+7\sqrt{5}}{2\sqrt{3}\cdot6\sqrt{5}}\frac{\sqrt{15}}{\sqrt{15}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3\sqrt{30}+35\sqrt{3}}{180}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{15}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 3 \sqrt{2} + 7 \sqrt{5}\right) } \cdot \sqrt{15} = \color{blue}{ 3 \sqrt{2}} \cdot \sqrt{15}+\color{blue}{ 7 \sqrt{5}} \cdot \sqrt{15} = \\ = 3 \sqrt{30} + 35 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ 12 \sqrt{15} } \cdot \sqrt{15} = 180 $$ |
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