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