Question
Answer
$$\dfrac{4\sqrt{2}}{\sqrt{15}-3\sqrt{2}}=-\dfrac{4\sqrt{30}+24}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{2}}{\sqrt{15}-3\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{2}}{\sqrt{15}-3\sqrt{2}}\frac{\sqrt{15}+3\sqrt{2}}{\sqrt{15}+3\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{30}+24}{15+3\sqrt{30}-3\sqrt{30}-18} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4\sqrt{30}+24}{-3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{4\sqrt{30}+24}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{15} + 3 \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 \sqrt{2} } \cdot \left( \sqrt{15} + 3 \sqrt{2}\right) = \color{blue}{ 4 \sqrt{2}} \cdot \sqrt{15}+\color{blue}{ 4 \sqrt{2}} \cdot 3 \sqrt{2} = \\ = 4 \sqrt{30} + 24 $$ 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 | Place a negative sign in front of a fraction. |
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