Question
Answer
$$\dfrac{10}{\sqrt{3}+8\sqrt{2}}=\dfrac{-10\sqrt{3}+80\sqrt{2}}{125}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10}{\sqrt{3}+8\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10}{\sqrt{3}+8\sqrt{2}}\frac{\sqrt{3}-8\sqrt{2}}{\sqrt{3}-8\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10\sqrt{3}-80\sqrt{2}}{3-8\sqrt{6}+8\sqrt{6}-128} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{10\sqrt{3}-80\sqrt{2}}{-125} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-10\sqrt{3}+80\sqrt{2}}{125}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3}- 8 \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 10 } \cdot \left( \sqrt{3}- 8 \sqrt{2}\right) = \color{blue}{10} \cdot \sqrt{3}+\color{blue}{10} \cdot- 8 \sqrt{2} = \\ = 10 \sqrt{3}- 80 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{3} + 8 \sqrt{2}\right) } \cdot \left( \sqrt{3}- 8 \sqrt{2}\right) = \color{blue}{ \sqrt{3}} \cdot \sqrt{3}+\color{blue}{ \sqrt{3}} \cdot- 8 \sqrt{2}+\color{blue}{ 8 \sqrt{2}} \cdot \sqrt{3}+\color{blue}{ 8 \sqrt{2}} \cdot- 8 \sqrt{2} = \\ = 3- 8 \sqrt{6} + 8 \sqrt{6}-128 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator