Question
Answer
$$\dfrac{7\sqrt{8}\cdot2\sqrt{6}}{1}=56\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7\sqrt{8}\cdot2\sqrt{6}}{1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}14\sqrt{48} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}14\cdot \sqrt{ 16 \cdot 3 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}14\cdot \sqrt{ 16 } \cdot \sqrt{ 3 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}14\cdot4 \sqrt{ 3 } \xlongequal{ } \\[1 em] & \xlongequal{ }56\sqrt{3}\end{aligned} $$ | |
| ① | Remove 1 from denominator. |
| ② | Factor out the largest perfect square of 48. ( in this example we factored out $ 16 $ ) |
| ③ | Rewrite $ \sqrt{ 16 \cdot 3 } $ as the product of two radicals. |
| ④ | The square root of $ 16 $ is $ 4 $. |
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