Answer
$$\frac{13\sqrt{15}-2\sqrt{10}}{4\sqrt{75}}=\frac{39\sqrt{5}-2\sqrt{30}}{60}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{13\sqrt{15}-2\sqrt{10}}{4\sqrt{75}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{13\sqrt{15}-2\sqrt{10}}{4\sqrt{75}}\frac{\sqrt{75}}{\sqrt{75}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{195\sqrt{5}-10\sqrt{30}}{300} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{39\sqrt{5}-2\sqrt{30}}{60}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{75}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 13 \sqrt{15}- 2 \sqrt{10}\right) } \cdot \sqrt{75} = \color{blue}{ 13 \sqrt{15}} \cdot \sqrt{75}\color{blue}{- 2 \sqrt{10}} \cdot \sqrt{75} = \\ = 195 \sqrt{5}- 10 \sqrt{30} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{75} } \cdot \sqrt{75} = 300 $$ |
| ③ | Divide both numerator and denominator by 5. |
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