Mathematics - Binomial Theorem Question with Solution | TestHub

$S=(2+\sqrt{3}{)}^8$
For sum of rational terms
$\begin{array}{rl}& ={}^8{\mathrm{C}}_0(2{)}^8+{}^8{\mathrm{C}}_2(2{)}^6\cdot (\sqrt{3}{)}^2+{}^8{\mathrm{C}}_4(2{)}^4(\sqrt{3}{)}^4\\ & +{}^8{\mathrm{C}}_6(2{)}^2(\sqrt{3}{)}^6+{}^8{\mathrm{C}}_8(\sqrt{3}{)}^8\\ & =2^8+28\times 2^6\cdot 3+70.2^4\cdot 9+28.2^2.27+81\\ & =256+5376+10080+3024+81\\ & =18817\end{array}$