Answer
$$\frac{4\sqrt{45}}{5\sqrt{8}}=\frac{3\sqrt{10}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{45}}{5\sqrt{8}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{45}}{5\sqrt{8}}\frac{\sqrt{8}}{\sqrt{8}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24\sqrt{10}}{40} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 24 \sqrt{ 10 } : \color{blue}{ 8 } } { 40 : \color{blue}{ 8 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3\sqrt{10}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{8}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 \sqrt{45} } \cdot \sqrt{8} = 24 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{8} } \cdot \sqrt{8} = 40 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 8 } $. |
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