Question
Answer
$$\dfrac{9\sqrt{45}}{3\sqrt{8}}=\dfrac{9\sqrt{10}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{9\sqrt{45}}{3\sqrt{8}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{9\sqrt{45}}{3\sqrt{8}}\frac{\sqrt{8}}{\sqrt{8}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{54\sqrt{10}}{24} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 54 \sqrt{ 10 } : \color{blue}{ 6 } } { 24 : \color{blue}{ 6 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{9\sqrt{10}}{4}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{8}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 9 \sqrt{45} } \cdot \sqrt{8} = 54 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{8} } \cdot \sqrt{8} = 24 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 6 } $. |
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