Answer
$$7\sqrt{600}=70\sqrt{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7\sqrt{600}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}7\cdot \sqrt{ 100 \cdot 6 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}7\cdot \sqrt{ 100 } \cdot \sqrt{ 6 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}7\cdot10 \sqrt{ 6 } \xlongequal{ } \\[1 em] & \xlongequal{ }70\sqrt{6}\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 600. ( in this example we factored out $ 100 $ ) |
| ② | Rewrite $ \sqrt{ 100 \cdot 6 } $ as the product of two radicals. |
| ③ | The square root of $ 100 $ is $ 10 $. |
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