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9+6\sqrt{7}+\left(\sqrt{7}\right)^{2}-6\sqrt{7}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+\sqrt{7}\right)^{2}.
9+6\sqrt{7}+7-6\sqrt{7}
The square of \sqrt{7} is 7.
16+6\sqrt{7}-6\sqrt{7}
Add 9 and 7 to get 16.
16
Combine 6\sqrt{7} and -6\sqrt{7} to get 0.