Answer
$$\frac{8}{7-3\sqrt{5}}=\frac{56+24\sqrt{5}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8}{7-3\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8}{7-3\sqrt{5}}\frac{7+3\sqrt{5}}{7+3\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{56+24\sqrt{5}}{49+21\sqrt{5}-21\sqrt{5}-45} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{56+24\sqrt{5}}{4}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 7 + 3 \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 8 } \cdot \left( 7 + 3 \sqrt{5}\right) = \color{blue}{8} \cdot7+\color{blue}{8} \cdot 3 \sqrt{5} = \\ = 56 + 24 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \left( 7- 3 \sqrt{5}\right) } \cdot \left( 7 + 3 \sqrt{5}\right) = \color{blue}{7} \cdot7+\color{blue}{7} \cdot 3 \sqrt{5}\color{blue}{- 3 \sqrt{5}} \cdot7\color{blue}{- 3 \sqrt{5}} \cdot 3 \sqrt{5} = \\ = 49 + 21 \sqrt{5}- 21 \sqrt{5}-45 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator