Evaluate
12\sqrt{7}+37\approx 68.749015733
Expand
12 \sqrt{7} + 37 = 68.749015733
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9+12\sqrt{7}+4\left(\sqrt{7}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+2\sqrt{7}\right)^{2}.
9+12\sqrt{7}+4\times 7
The square of \sqrt{7} is 7.
9+12\sqrt{7}+28
Multiply 4 and 7 to get 28.
37+12\sqrt{7}
Add 9 and 28 to get 37.
9+12\sqrt{7}+4\left(\sqrt{7}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+2\sqrt{7}\right)^{2}.
9+12\sqrt{7}+4\times 7
The square of \sqrt{7} is 7.
9+12\sqrt{7}+28
Multiply 4 and 7 to get 28.
37+12\sqrt{7}
Add 9 and 28 to get 37.
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