Question

The integral Part of ${(\sqrt{3}+1)}^6$ is

• A. $416$
• B. $120\sqrt{3}$
• C. $415$
• D. None of these

Answer 1

The correct option is C $415$

$(1+\sqrt{3}{)}^6$
$=1+6\sqrt{3}+15(\sqrt{3}{)}^2+20(\sqrt{3}{)}^3+15(\sqrt{3}{)}^4+6(\sqrt{3}{)}^5+(\sqrt{3}{)}^6$
$=1+6\sqrt{3}+45+60\sqrt{3}+135+54\sqrt{3}+27$
$=120\sqrt{3}+208$
$=208+120\left(1.732\right)$
$=\mathrm{415.8460..}$
Hence integral part is $415$