Question
Answer
$$\dfrac{\sqrt{2}+10}{\sqrt{2}-10}=-\dfrac{51+10\sqrt{2}}{49}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{2}+10}{\sqrt{2}-10}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{2}+10}{\sqrt{2}-10}\frac{\sqrt{2}+10}{\sqrt{2}+10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2+10\sqrt{2}+10\sqrt{2}+100}{2+10\sqrt{2}-10\sqrt{2}-100} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{102+20\sqrt{2}}{-98} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{51+10\sqrt{2}}{-49} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-\frac{51+10\sqrt{2}}{49}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2} + 10} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{2} + 10\right) } \cdot \left( \sqrt{2} + 10\right) = \color{blue}{ \sqrt{2}} \cdot \sqrt{2}+\color{blue}{ \sqrt{2}} \cdot10+\color{blue}{10} \cdot \sqrt{2}+\color{blue}{10} \cdot10 = \\ = 2 + 10 \sqrt{2} + 10 \sqrt{2} + 100 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{2}-10\right) } \cdot \left( \sqrt{2} + 10\right) = \color{blue}{ \sqrt{2}} \cdot \sqrt{2}+\color{blue}{ \sqrt{2}} \cdot10\color{blue}{-10} \cdot \sqrt{2}\color{blue}{-10} \cdot10 = \\ = 2 + 10 \sqrt{2}- 10 \sqrt{2}-100 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 2. |
| ⑤ | Place a negative sign in front of a fraction. |
This page was created using
Rationalize Denominator Calculator