Evaluate
\left(4n+\sqrt{5}\right)^{2}
Expand
16n^{2}+8\sqrt{5}n+5
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\left(\sqrt{5}\right)^{2}+8\sqrt{5}n+16n^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{5}+4n\right)^{2}.
5+8\sqrt{5}n+16n^{2}
The square of \sqrt{5} is 5.
\left(\sqrt{5}\right)^{2}+8\sqrt{5}n+16n^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{5}+4n\right)^{2}.
5+8\sqrt{5}n+16n^{2}
The square of \sqrt{5} is 5.
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