Answer
$$\frac{5\sqrt{2}}{\sqrt{3}-2\sqrt{2}}=-\sqrt{6}-4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5\sqrt{2}}{\sqrt{3}-2\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5\sqrt{2}}{\sqrt{3}-2\sqrt{2}}\frac{\sqrt{3}+2\sqrt{2}}{\sqrt{3}+2\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5\sqrt{6}+20}{3+2\sqrt{6}-2\sqrt{6}-8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5\sqrt{6}+20}{-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{\sqrt{6}+4}{-1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-\frac{\sqrt{6}+4}{1} \xlongequal{ } \\[1 em] & \xlongequal{ }-(\sqrt{6}+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-\sqrt{6}-4\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{3} + 2 \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 \sqrt{2} } \cdot \left( \sqrt{3} + 2 \sqrt{2}\right) = \color{blue}{ 5 \sqrt{2}} \cdot \sqrt{3}+\color{blue}{ 5 \sqrt{2}} \cdot 2 \sqrt{2} = \\ = 5 \sqrt{6} + 20 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{3}- 2 \sqrt{2}\right) } \cdot \left( \sqrt{3} + 2 \sqrt{2}\right) = \color{blue}{ \sqrt{3}} \cdot \sqrt{3}+\color{blue}{ \sqrt{3}} \cdot 2 \sqrt{2}\color{blue}{- 2 \sqrt{2}} \cdot \sqrt{3}\color{blue}{- 2 \sqrt{2}} \cdot 2 \sqrt{2} = \\ = 3 + 2 \sqrt{6}- 2 \sqrt{6}-8 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 5. |
| ⑤ | Place a negative sign in front of a fraction. |
| ⑥ | Remove the parenthesis by changing the sign of each term within them. |
This page was created using
Rationalize Denominator Calculator