Evaluate
20\sqrt{6}+154\approx 202.989794856
Expand
20 \sqrt{6} + 154 = 202.989794856
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4+20\sqrt{6}+25\left(\sqrt{6}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2+5\sqrt{6}\right)^{2}.
4+20\sqrt{6}+25\times 6
The square of \sqrt{6} is 6.
4+20\sqrt{6}+150
Multiply 25 and 6 to get 150.
154+20\sqrt{6}
Add 4 and 150 to get 154.
4+20\sqrt{6}+25\left(\sqrt{6}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2+5\sqrt{6}\right)^{2}.
4+20\sqrt{6}+25\times 6
The square of \sqrt{6} is 6.
4+20\sqrt{6}+150
Multiply 25 and 6 to get 150.
154+20\sqrt{6}
Add 4 and 150 to get 154.
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