Question
Answer
$$\dfrac{\sqrt{81}}{\sqrt{48}}=\dfrac{3\sqrt{3}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{81}}{\sqrt{48}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{81}}{\sqrt{48}}\frac{\sqrt{48}}{\sqrt{48}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{36\sqrt{3}}{48} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 36 \sqrt{ 3 } : \color{blue}{ 12 } } { 48 : \color{blue}{ 12 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3\sqrt{3}}{4}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{48}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{81} } \cdot \sqrt{48} = 36 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \sqrt{48} } \cdot \sqrt{48} = 48 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 12 } $. |
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