Answer
$$\frac{54\sqrt{54}}{\sqrt{15}}=\frac{162\sqrt{10}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{54\sqrt{54}}{\sqrt{15}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{54\sqrt{54}}{\sqrt{15}}\frac{\sqrt{15}}{\sqrt{15}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{486\sqrt{10}}{15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 486 \sqrt{ 10 } : \color{blue}{ 3 } } { 15 : \color{blue}{ 3 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{162\sqrt{10}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{15}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 54 \sqrt{54} } \cdot \sqrt{15} = 486 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \sqrt{15} } \cdot \sqrt{15} = 15 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 3 } $. |
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