Answer
$$\frac{\sqrt{3}+3\sqrt{5}}{2\sqrt{8}}=\frac{\sqrt{6}+3\sqrt{10}}{8}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{3}+3\sqrt{5}}{2\sqrt{8}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{3}+3\sqrt{5}}{2\sqrt{8}}\frac{\sqrt{8}}{\sqrt{8}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2\sqrt{6}+6\sqrt{10}}{16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{6}+3\sqrt{10}}{8}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{8}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{3} + 3 \sqrt{5}\right) } \cdot \sqrt{8} = \color{blue}{ \sqrt{3}} \cdot \sqrt{8}+\color{blue}{ 3 \sqrt{5}} \cdot \sqrt{8} = \\ = 2 \sqrt{6} + 6 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{8} } \cdot \sqrt{8} = 16 $$ |
| ③ | Divide both numerator and denominator by 2. |
This page was created using
Rationalize Denominator Calculator