Evaluate
50\left(\sqrt{3}+2\right)\approx 186.602540378
Expand
50 \sqrt{3} + 100 = 186.602540378
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25\left(\sqrt{3}\right)^{2}+50\sqrt{3}+25
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5\sqrt{3}+5\right)^{2}.
25\times 3+50\sqrt{3}+25
The square of \sqrt{3} is 3.
75+50\sqrt{3}+25
Multiply 25 and 3 to get 75.
100+50\sqrt{3}
Add 75 and 25 to get 100.
25\left(\sqrt{3}\right)^{2}+50\sqrt{3}+25
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5\sqrt{3}+5\right)^{2}.
25\times 3+50\sqrt{3}+25
The square of \sqrt{3} is 3.
75+50\sqrt{3}+25
Multiply 25 and 3 to get 75.
100+50\sqrt{3}
Add 75 and 25 to get 100.
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