Question
Answer
$$\dfrac{8\sqrt{5}}{2\sqrt{36}}=\dfrac{2\sqrt{5}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8\sqrt{5}}{2\sqrt{36}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8\sqrt{5}}{2\sqrt{36}}\frac{\sqrt{36}}{\sqrt{36}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{48\sqrt{5}}{72} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 48 \sqrt{ 5 } : \color{blue}{ 24 } } { 72 : \color{blue}{ 24 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{5}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{36}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 8 \sqrt{5} } \cdot \sqrt{36} = 48 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{36} } \cdot \sqrt{36} = 72 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 24 } $. |
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