Question
Answer
$$\dfrac{\dfrac{1+\sqrt{25}}{4}-\dfrac{1-\sqrt{25}}{4}}{\sqrt{5}}=\dfrac{1}{2}\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{1+\sqrt{25}}{4}-\frac{1-\sqrt{25}}{4}}{\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{1+5-1+5}{4}}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{10}{4}}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\frac{10}{4}}{\sqrt{5}}\frac{\sqrt{5}}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{\frac{5}{2}\sqrt{5}}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{\frac{1}{2}\sqrt{5}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{1}{2}\sqrt{5}\end{aligned} $$ | |
| ① | $$ \frac{1+\sqrt{25}}{4}-\frac{1-\sqrt{25}}{4}
= \frac{1+\sqrt{25}}{4} \cdot \color{blue}{\frac{ 1 }{ 1}} - \frac{1-\sqrt{25}}{4} \cdot \color{blue}{\frac{ 1 }{ 1}}
= \frac{1+5-1+5}{4} $$ |
| ② | Simplify numerator $$ \, \color{blue}{ \cancel{1}} \,+ \color{green}{5} \, \color{orange}{ -\cancel{1}} \,+ \color{orange}{5} = \color{orange}{10} $$ |
| ③ | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{5}} $$. |
| ④ | Multiply in a numerator. $$ \color{blue}{ \frac{ 5 }{ 2 } } \cdot \sqrt{5} = \frac{ 5 }{ 2 } \sqrt{ 5 } $$ Simplify denominator. $$ \color{blue}{ \sqrt{5} } \cdot \sqrt{5} = 5 $$ |
| ⑤ | Divide both numerator and denominator by 5. |
| ⑥ | Remove 1 from denominator. |
This page was created using
Simplify Radical Expression