Answer
$$\frac{\sqrt{15}^3}{\sqrt{6}^3}=\frac{5\sqrt{10}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{15}^3}{\sqrt{6}^3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15\sqrt{15}}{6\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{15\sqrt{15}}{6\sqrt{6}}\frac{\sqrt{6}}{\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{45\sqrt{10}}{36} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{ 45 \sqrt{ 10 } : \color{blue}{ 9 } } { 36 : \color{blue}{ 9 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5\sqrt{10}}{4}\end{aligned} $$ | |
| ① | $$ \sqrt{15}^3 =
\sqrt{15} ^2 \cdot \sqrt{15} =
\lvert 15 \rvert \cdot \sqrt{15} =
15\sqrt{15} $$ |
| ② | $$ \sqrt{6}^3 =
\sqrt{6} ^2 \cdot \sqrt{6} =
\lvert 6 \rvert \cdot \sqrt{6} =
6\sqrt{6} $$ |
| ③ | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}} $$. |
| ④ | Multiply in a numerator. $$ \color{blue}{ 15 \sqrt{15} } \cdot \sqrt{6} = 45 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ 6 \sqrt{6} } \cdot \sqrt{6} = 36 $$ |
| ⑤ | Divide numerator and denominator by $ \color{blue}{ 9 } $. |
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