The sum of all rational terms in the expansion of (2+√(3)) 8 is

Mathematics · Binomial Theorem

JEE Main 2025 — 3 April, Morning Shift — Question 23

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

$S=(2+\sqrt{3})^{8}$

For sum of rational terms

$={ }^{8} \mathrm{C}_{0}(2)^{8}+{ }^{8} \mathrm{C}_{2}(2)^{6} \cdot(\sqrt{3})^{2}+{ }^{8} \mathrm{C}_{4}(2)^{4}(\sqrt{3})^{4}$

+{ }^{8} \mathrm{C}_{6}(2)^{2}(\sqrt{3})^{6}+{ }^{8} \mathrm{C}_{8}(\sqrt{3})^{8}

$=2^{8}+28 \times 2^{6} .3+70.2^{4} .9+28.2^{2} .27+81$

$=256+5376+10080+3024+81$

$=18817$

Answer key and solution verified before publishing.

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