Question
Answer
$$\dfrac{(2\sqrt{5})^3}{\sqrt{11}}=\dfrac{40\sqrt{55}}{11}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(2\sqrt{5})^3}{\sqrt{11}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{40\sqrt{5}}{\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{40\sqrt{5}}{\sqrt{11}}\frac{\sqrt{11}}{\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{40\sqrt{55}}{11}\end{aligned} $$ | |
| ① | $$ (2\sqrt{5})^3 =
2^{ 3 } \cdot \sqrt{5} ^ { 3 } =
2^{ 3 } \sqrt{5} ^2 \cdot \sqrt{5} =
2^{ 3 } \lvert 5 \rvert \cdot \sqrt{5} =
40\sqrt{5} $$ |
| ② | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{11}} $$. |
| ③ | Multiply in a numerator. $$ \color{blue}{ 40 \sqrt{5} } \cdot \sqrt{11} = 40 \sqrt{55} $$ Simplify denominator. $$ \color{blue}{ \sqrt{11} } \cdot \sqrt{11} = 11 $$ |
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