Answer
$$5\sqrt{84}=10\sqrt{21}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\sqrt{84}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5\cdot \sqrt{ 4 \cdot 21 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5\cdot \sqrt{ 4 } \cdot \sqrt{ 21 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5\cdot2 \sqrt{ 21 } \xlongequal{ } \\[1 em] & \xlongequal{ }10\sqrt{21}\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 84. ( in this example we factored out $ 4 $ ) |
| ② | Rewrite $ \sqrt{ 4 \cdot 21 } $ as the product of two radicals. |
| ③ | The square root of $ 4 $ is $ 2 $. |
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Simplify Radical Expression