Question
Answer
$$\dfrac{10\sqrt{2}}{-3\sqrt{5}}=-\dfrac{2\sqrt{10}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10\sqrt{2}}{-3\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10\sqrt{2}}{-3\sqrt{5}}\frac{\sqrt{5}}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10\sqrt{10}}{-15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-\frac{10\sqrt{10}}{15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{ 10 \sqrt{ 10 } : \color{blue}{ 5 } } { 15 : \color{blue}{ 5 }} \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{2\sqrt{10}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 10 \sqrt{2} } \cdot \sqrt{5} = 10 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ - 3 \sqrt{5} } \cdot \sqrt{5} = -15 $$ |
| ③ | Place a negative sign in front of a fraction. |
| ④ | Divide numerator and denominator by $ \color{blue}{ 5 } $. |
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