Question
Answer
$$\dfrac{\sqrt{5}+4}{4\sqrt{17}}=\dfrac{\sqrt{85}+4\sqrt{17}}{68}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{5}+4}{4\sqrt{17}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{5}+4}{4\sqrt{17}}\frac{\sqrt{17}}{\sqrt{17}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\sqrt{85}+4\sqrt{17}}{68}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{17}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{5} + 4\right) } \cdot \sqrt{17} = \color{blue}{ \sqrt{5}} \cdot \sqrt{17}+\color{blue}{4} \cdot \sqrt{17} = \\ = \sqrt{85} + 4 \sqrt{17} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{17} } \cdot \sqrt{17} = 68 $$ |
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