Question
Answer
$$\dfrac{7\sqrt{2}}{\sqrt{6}+8}=\dfrac{-14\sqrt{3}+56\sqrt{2}}{58}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7\sqrt{2}}{\sqrt{6}+8}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7\sqrt{2}}{\sqrt{6}+8}\frac{\sqrt{6}-8}{\sqrt{6}-8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{14\sqrt{3}-56\sqrt{2}}{6-8\sqrt{6}+8\sqrt{6}-64} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{14\sqrt{3}-56\sqrt{2}}{-58} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-14\sqrt{3}+56\sqrt{2}}{58}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}-8} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 7 \sqrt{2} } \cdot \left( \sqrt{6}-8\right) = \color{blue}{ 7 \sqrt{2}} \cdot \sqrt{6}+\color{blue}{ 7 \sqrt{2}} \cdot-8 = \\ = 14 \sqrt{3}- 56 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{6} + 8\right) } \cdot \left( \sqrt{6}-8\right) = \color{blue}{ \sqrt{6}} \cdot \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot-8+\color{blue}{8} \cdot \sqrt{6}+\color{blue}{8} \cdot-8 = \\ = 6- 8 \sqrt{6} + 8 \sqrt{6}-64 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator