Perform the indicated operation. Assume that all variables represent positive numbers.
-$\sqrt { 300 } + \sqrt { 720 } + \sqrt { 192 } + 4 \sqrt { 20 }$

Question

Quizplus · Accepted Answer

First, simplify each square root by factoring out perfect squares: $\sqrt{300} = \sqrt{100 \cdot 3} = 10\sqrt{3}$, $\sqrt{720} = \sqrt{144 \cdot 5} = 12\sqrt{5}$, $\sqrt{192} = \sqrt{64 \cdot 3} = 8\sqrt{3}$, and $4\sqrt{20} = 4\sqrt{4 \cdot 5} = 8\sqrt{5}$. Adding these together gives $10\sqrt{3} + 8\sqrt{3} = 18\sqrt{3}$ and $12\sqrt{5} + 8\sqrt{5} = 20\sqrt{5}$, so the answer is $18\sqrt{3} + 20\sqrt{5}$.

Perform the Indicated Operation 300+720+192+420\sqrt { 300 } + \sqrt { 720 } + \sqrt { 192 } + 4 \sqrt { 20 }300​+720​+192​+420​

Perform the Indicated Operation $\sqrt { 300 } + \sqrt { 720 } + \sqrt { 192 } + 4 \sqrt { 20 }$