Evaluate
12\sqrt{3}+31\approx 51.784609691
Expand
12 \sqrt{3} + 31 = 51.784609691
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\left(3\sqrt{3}+2\right)^{2}
Combine 2\sqrt{3} and \sqrt{3} to get 3\sqrt{3}.
9\left(\sqrt{3}\right)^{2}+12\sqrt{3}+4
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3\sqrt{3}+2\right)^{2}.
9\times 3+12\sqrt{3}+4
The square of \sqrt{3} is 3.
27+12\sqrt{3}+4
Multiply 9 and 3 to get 27.
31+12\sqrt{3}
Add 27 and 4 to get 31.
\left(3\sqrt{3}+2\right)^{2}
Combine 2\sqrt{3} and \sqrt{3} to get 3\sqrt{3}.
9\left(\sqrt{3}\right)^{2}+12\sqrt{3}+4
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3\sqrt{3}+2\right)^{2}.
9\times 3+12\sqrt{3}+4
The square of \sqrt{3} is 3.
27+12\sqrt{3}+4
Multiply 9 and 3 to get 27.
31+12\sqrt{3}
Add 27 and 4 to get 31.
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Limits
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