Evaluate
84\sqrt{3}+183\approx 328.492267836
Expand
84 \sqrt{3} + 183 = 328.492267836
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36+84\sqrt{3}+49\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6+7\sqrt{3}\right)^{2}.
36+84\sqrt{3}+49\times 3
The square of \sqrt{3} is 3.
36+84\sqrt{3}+147
Multiply 49 and 3 to get 147.
183+84\sqrt{3}
Add 36 and 147 to get 183.
36+84\sqrt{3}+49\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(6+7\sqrt{3}\right)^{2}.
36+84\sqrt{3}+49\times 3
The square of \sqrt{3} is 3.
36+84\sqrt{3}+147
Multiply 49 and 3 to get 147.
183+84\sqrt{3}
Add 36 and 147 to get 183.
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