Answer
$$\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}=-\sqrt{30}+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}\frac{\sqrt{15}-3\sqrt{2}}{\sqrt{15}-3\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3\sqrt{30}-18}{15-3\sqrt{30}+3\sqrt{30}-18} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3\sqrt{30}-18}{-3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{\sqrt{30}-6}{-1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{-\sqrt{30}+6}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-\sqrt{30}+6\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{15}- 3 \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 \sqrt{2} } \cdot \left( \sqrt{15}- 3 \sqrt{2}\right) = \color{blue}{ 3 \sqrt{2}} \cdot \sqrt{15}+\color{blue}{ 3 \sqrt{2}} \cdot- 3 \sqrt{2} = \\ = 3 \sqrt{30}-18 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{15} + 3 \sqrt{2}\right) } \cdot \left( \sqrt{15}- 3 \sqrt{2}\right) = \color{blue}{ \sqrt{15}} \cdot \sqrt{15}+\color{blue}{ \sqrt{15}} \cdot- 3 \sqrt{2}+\color{blue}{ 3 \sqrt{2}} \cdot \sqrt{15}+\color{blue}{ 3 \sqrt{2}} \cdot- 3 \sqrt{2} = \\ = 15- 3 \sqrt{30} + 3 \sqrt{30}-18 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 3. |
| ⑤ | Multiply both numerator and denominator by -1. |
| ⑥ | Remove 1 from denominator. |
This page was created using
Rationalize Denominator Calculator