Question
Answer
$$\dfrac{\sqrt{24}}{\sqrt{57}}=\dfrac{2\sqrt{38}}{19}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{24}}{\sqrt{57}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{24}}{\sqrt{57}}\frac{\sqrt{57}}{\sqrt{57}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{38}}{57} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 6 \sqrt{ 38 } : \color{blue}{ 3 } } { 57 : \color{blue}{ 3 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{38}}{19}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{57}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{24} } \cdot \sqrt{57} = 6 \sqrt{38} $$ Simplify denominator. $$ \color{blue}{ \sqrt{57} } \cdot \sqrt{57} = 57 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 3 } $. |
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