Question
Answer
$$\dfrac{8\sqrt{5}}{5\sqrt{16}}=\dfrac{2\sqrt{5}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8\sqrt{5}}{5\sqrt{16}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8\sqrt{5}}{5\sqrt{16}}\frac{\sqrt{16}}{\sqrt{16}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{32\sqrt{5}}{80} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 32 \sqrt{ 5 } : \color{blue}{ 16 } } { 80 : \color{blue}{ 16 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{5}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{16}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 8 \sqrt{5} } \cdot \sqrt{16} = 32 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{16} } \cdot \sqrt{16} = 80 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 16 } $. |
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