Evaluate
104\sqrt{3}+217\approx 397.133283987
Expand
104 \sqrt{3} + 217 = 397.133283987
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169+104\sqrt{3}+16\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(13+4\sqrt{3}\right)^{2}.
169+104\sqrt{3}+16\times 3
The square of \sqrt{3} is 3.
169+104\sqrt{3}+48
Multiply 16 and 3 to get 48.
217+104\sqrt{3}
Add 169 and 48 to get 217.
169+104\sqrt{3}+16\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(13+4\sqrt{3}\right)^{2}.
169+104\sqrt{3}+16\times 3
The square of \sqrt{3} is 3.
169+104\sqrt{3}+48
Multiply 16 and 3 to get 48.
217+104\sqrt{3}
Add 169 and 48 to get 217.
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