A) 75
B) 50
C) 76
D) 51
E) 152
Correct Answer: E
Solution :
Now,\[{{(\sqrt{3}+1)}^{5}}={{(\sqrt{3})}^{2}}{{+}^{5}}{{C}_{1}}{{(\sqrt{3})}^{4}}{{+}^{5}}{{C}_{2}}{{(\sqrt{3})}^{3}}\] \[{{+}^{5}}{{C}_{3}}{{(\sqrt{3})}^{2}}{{+}^{5}}{{C}_{4}}(\sqrt{3}){{+}^{5}}{{C}_{5}}\] \[=9\sqrt{3}+45+30\sqrt{3}+30+5\sqrt{3}+1\] \[=76+44\sqrt{3}\] \[\therefore \] \[[{{(\sqrt{3}+1)}^{2}}]=[76+44\sqrt{3}]\] \[=[76]+[44\times 1.732]\] \[=76+[76.2]\] \[=76+76=152\]
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