Evaluate
40\sqrt{7}+128\approx 233.830052443
Expand
40 \sqrt{7} + 128 = 233.830052443
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100+40\sqrt{7}+4\left(\sqrt{7}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(10+2\sqrt{7}\right)^{2}.
100+40\sqrt{7}+4\times 7
The square of \sqrt{7} is 7.
100+40\sqrt{7}+28
Multiply 4 and 7 to get 28.
128+40\sqrt{7}
Add 100 and 28 to get 128.
100+40\sqrt{7}+4\left(\sqrt{7}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(10+2\sqrt{7}\right)^{2}.
100+40\sqrt{7}+4\times 7
The square of \sqrt{7} is 7.
100+40\sqrt{7}+28
Multiply 4 and 7 to get 28.
128+40\sqrt{7}
Add 100 and 28 to get 128.
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