Question
Answer
$$\dfrac{5-\sqrt{4}}{5+\sqrt{4}}=\dfrac{3}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5-\sqrt{4}}{5+\sqrt{4}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5-\sqrt{4}}{5+\sqrt{4}}\frac{5-\sqrt{4}}{5-\sqrt{4}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{25-10-10+4}{25-10+10-4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{9}{21} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 9 : \color{orangered}{ 3 } }{ 21 : \color{orangered}{ 3 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3}{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5- \sqrt{4}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 5- \sqrt{4}\right) } \cdot \left( 5- \sqrt{4}\right) = \color{blue}{5} \cdot5+\color{blue}{5} \cdot- \sqrt{4}\color{blue}{- \sqrt{4}} \cdot5\color{blue}{- \sqrt{4}} \cdot- \sqrt{4} = \\ = 25-10-10 + 4 $$ Simplify denominator. $$ \color{blue}{ \left( 5 + \sqrt{4}\right) } \cdot \left( 5- \sqrt{4}\right) = \color{blue}{5} \cdot5+\color{blue}{5} \cdot- \sqrt{4}+\color{blue}{ \sqrt{4}} \cdot5+\color{blue}{ \sqrt{4}} \cdot- \sqrt{4} = \\ = 25-10 + 10-4 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both the top and bottom numbers by $ \color{orangered}{ 3 } $. |
This page was created using
Rationalize Denominator Calculator