Question
Answer
$$\dfrac{15\sqrt{2}}{\sqrt{24}}=\dfrac{5\sqrt{3}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{15\sqrt{2}}{\sqrt{24}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{15\sqrt{2}}{\sqrt{24}}\frac{\sqrt{24}}{\sqrt{24}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{60\sqrt{3}}{24} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 60 \sqrt{ 3 } : \color{blue}{ 12 } } { 24 : \color{blue}{ 12 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5\sqrt{3}}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{24}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 15 \sqrt{2} } \cdot \sqrt{24} = 60 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \sqrt{24} } \cdot \sqrt{24} = 24 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 12 } $. |
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