Evaluate
72\sqrt{5}+161\approx 321.99689438
Expand
72 \sqrt{5} + 161 = 321.99689438
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81+72\sqrt{5}+16\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(9+4\sqrt{5}\right)^{2}.
81+72\sqrt{5}+16\times 5
The square of \sqrt{5} is 5.
81+72\sqrt{5}+80
Multiply 16 and 5 to get 80.
161+72\sqrt{5}
Add 81 and 80 to get 161.
81+72\sqrt{5}+16\left(\sqrt{5}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(9+4\sqrt{5}\right)^{2}.
81+72\sqrt{5}+16\times 5
The square of \sqrt{5} is 5.
81+72\sqrt{5}+80
Multiply 16 and 5 to get 80.
161+72\sqrt{5}
Add 81 and 80 to get 161.
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