Evaluate
8\left(\sqrt{3}+2\right)\approx 29.856406461
Expand
8 \sqrt{3} + 16 = 29.856406461
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4\left(\left(\sqrt{3}\right)^{2}+2\sqrt{3}+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{3}+1\right)^{2}.
4\left(3+2\sqrt{3}+1\right)
The square of \sqrt{3} is 3.
4\left(4+2\sqrt{3}\right)
Add 3 and 1 to get 4.
16+8\sqrt{3}
Use the distributive property to multiply 4 by 4+2\sqrt{3}.
4\left(\left(\sqrt{3}\right)^{2}+2\sqrt{3}+1\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{3}+1\right)^{2}.
4\left(3+2\sqrt{3}+1\right)
The square of \sqrt{3} is 3.
4\left(4+2\sqrt{3}\right)
Add 3 and 1 to get 4.
16+8\sqrt{3}
Use the distributive property to multiply 4 by 4+2\sqrt{3}.
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