The sum of all rational terms in the expansion of $(2+\sqrt{3})^8$ is

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Aicharya · Accepted Answer

$S=(2+\sqrt{3})^8$ For sum of rational terms $\begin{aligned} & ={ }^8 \mathrm{C}_0(2)^8+{ }^8 \mathrm{C}_2(2)^6 \cdot(\sqrt{3})^2+{ }^8 \mathrm{C}_4(2)^4(\sqrt{3})^4 \ & \quad+\quad{ }^8 \mathrm{C}_6(2)^2(\sqrt{3})^6+{ }^8 \mathrm{C}_8(\sqrt{3})^8 \ & =2^8+28 	imes 2^6 \cdot 3+70.2^4 \cdot 9+28.2^2 .27+81 \ & =256+5376+10080+3024+81 \ & =18817\end{aligned}$

The sum of all rational terms in the expansion of $(2+\sqrt{3})^8$ is

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