Question
Answer
$$\dfrac{2}{5+\sqrt{10}}=\dfrac{10-2\sqrt{10}}{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{5+\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2}{5+\sqrt{10}}\frac{5-\sqrt{10}}{5-\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10-2\sqrt{10}}{25-5\sqrt{10}+5\sqrt{10}-10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{10-2\sqrt{10}}{15}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5- \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 } \cdot \left( 5- \sqrt{10}\right) = \color{blue}{2} \cdot5+\color{blue}{2} \cdot- \sqrt{10} = \\ = 10- 2 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \left( 5 + \sqrt{10}\right) } \cdot \left( 5- \sqrt{10}\right) = \color{blue}{5} \cdot5+\color{blue}{5} \cdot- \sqrt{10}+\color{blue}{ \sqrt{10}} \cdot5+\color{blue}{ \sqrt{10}} \cdot- \sqrt{10} = \\ = 25- 5 \sqrt{10} + 5 \sqrt{10}-10 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator