Evaluate
4\sqrt{3}+13\approx 19.92820323
Expand
4 \sqrt{3} + 13 = 19.92820323
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4\left(\sqrt{3}\right)^{2}+4\sqrt{3}+1
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2\sqrt{3}+1\right)^{2}.
4\times 3+4\sqrt{3}+1
The square of \sqrt{3} is 3.
12+4\sqrt{3}+1
Multiply 4 and 3 to get 12.
13+4\sqrt{3}
Add 12 and 1 to get 13.
4\left(\sqrt{3}\right)^{2}+4\sqrt{3}+1
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2\sqrt{3}+1\right)^{2}.
4\times 3+4\sqrt{3}+1
The square of \sqrt{3} is 3.
12+4\sqrt{3}+1
Multiply 4 and 3 to get 12.
13+4\sqrt{3}
Add 12 and 1 to get 13.
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