Answer
$$\frac{(\sqrt{3}-\sqrt{5})(\sqrt{45}+5\sqrt{3}+14+2\sqrt{15}+\sqrt{75}+5\sqrt{5}+4\sqrt{15}-\sqrt{5})}{1}=-3\sqrt{15}-5-16\sqrt{3}+4\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(\sqrt{3}-\sqrt{5})(\sqrt{45}+5\sqrt{3}+14+2\sqrt{15}+\sqrt{75}+5\sqrt{5}+4\sqrt{15}-\sqrt{5})}{1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{15}+15+14\sqrt{3}+6\sqrt{5}+15+5\sqrt{15}+12\sqrt{5}-\sqrt{15}-15-5\sqrt{15}-14\sqrt{5}-10\sqrt{3}-5\sqrt{15}-25-20\sqrt{3}+5}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-3\sqrt{15}-5-16\sqrt{3}+4\sqrt{5}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( \sqrt{3}- \sqrt{5}\right) } \cdot \left( \sqrt{45} + 5 \sqrt{3} + 14 + 2 \sqrt{15} + \sqrt{75} + 5 \sqrt{5} + 4 \sqrt{15}- \sqrt{5}\right) = \color{blue}{ \sqrt{3}} \cdot \sqrt{45}+\color{blue}{ \sqrt{3}} \cdot 5 \sqrt{3}+\color{blue}{ \sqrt{3}} \cdot14+\color{blue}{ \sqrt{3}} \cdot 2 \sqrt{15}+\color{blue}{ \sqrt{3}} \cdot \sqrt{75}+\color{blue}{ \sqrt{3}} \cdot 5 \sqrt{5}+\color{blue}{ \sqrt{3}} \cdot 4 \sqrt{15}+\color{blue}{ \sqrt{3}} \cdot- \sqrt{5}\color{blue}{- \sqrt{5}} \cdot \sqrt{45}\color{blue}{- \sqrt{5}} \cdot 5 \sqrt{3}\color{blue}{- \sqrt{5}} \cdot14\color{blue}{- \sqrt{5}} \cdot 2 \sqrt{15}\color{blue}{- \sqrt{5}} \cdot \sqrt{75}\color{blue}{- \sqrt{5}} \cdot 5 \sqrt{5}\color{blue}{- \sqrt{5}} \cdot 4 \sqrt{15}\color{blue}{- \sqrt{5}} \cdot- \sqrt{5} = \\ = 3 \sqrt{15} + 15 + 14 \sqrt{3} + 6 \sqrt{5} + 15 + 5 \sqrt{15} + 12 \sqrt{5}- \sqrt{15}-15- 5 \sqrt{15}- 14 \sqrt{5}- 10 \sqrt{3}- 5 \sqrt{15}-25- 20 \sqrt{3} + 5 $$ |
| ② | Remove 1 from denominator. |
This page was created using
Rationalize Denominator Calculator