Question
Answer
$$\dfrac{\dfrac{3}{2}}{\sqrt{\dfrac{18}{125}}}=\dfrac{\dfrac{1}{50}\sqrt{10}}{\dfrac{2}{125}}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{3}{2}}{\sqrt{\frac{18}{125}}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{3}{2}}{\sqrt{\frac{18}{125}}}\frac{\sqrt{\frac{18}{125}}}{\sqrt{\frac{18}{125}}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{9}{50}\sqrt{10}}{\frac{18}{125}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\frac{1}{50}\sqrt{10}}{\frac{2}{125}}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{\frac{ 18 }{ 125 }}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \frac{ 3 }{ 2 } } \cdot \sqrt{\frac{ 18 }{ 125 }} = \frac{ 9 }{ 50 } \sqrt{ 10 } $$ Simplify denominator. $$ \color{blue}{ \sqrt{\frac{ 18 }{ 125 }} } \cdot \sqrt{\frac{ 18 }{ 125 }} = \frac{ 18 }{ 125 } $$ |
| ③ | Divide both numerator and denominator by 9. |
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