Question
Answer
$$\dfrac{8\sqrt{9}}{9\sqrt{2}}=\dfrac{4\sqrt{2}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8\sqrt{9}}{9\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8\sqrt{9}}{9\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24\sqrt{2}}{18} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 24 \sqrt{ 2 } : \color{blue}{ 6 } } { 18 : \color{blue}{ 6 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4\sqrt{2}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 8 \sqrt{9} } \cdot \sqrt{2} = 24 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 9 \sqrt{2} } \cdot \sqrt{2} = 18 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 6 } $. |
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