Answer
$$\frac{3\sqrt{6}-5\sqrt{5}}{4\sqrt{10}}=\frac{6\sqrt{15}-25\sqrt{2}}{40}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{6}-5\sqrt{5}}{4\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{6}-5\sqrt{5}}{4\sqrt{10}}\frac{\sqrt{10}}{\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{15}-25\sqrt{2}}{40}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 3 \sqrt{6}- 5 \sqrt{5}\right) } \cdot \sqrt{10} = \color{blue}{ 3 \sqrt{6}} \cdot \sqrt{10}\color{blue}{- 5 \sqrt{5}} \cdot \sqrt{10} = \\ = 6 \sqrt{15}- 25 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{10} } \cdot \sqrt{10} = 40 $$ |
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