A) 40
B) 44
C) 48
D) 52
Correct Answer: D
Solution :
\[a=\sqrt{7+2\times \sqrt{4}\times \sqrt{3}}=\sqrt{4+3+2\times 2\times \sqrt{3}}\] \[=\sqrt{{{(2+\sqrt{3})}^{2}}}=2+\sqrt{3}\] \[\therefore \] \[b=\sqrt{7}-2\sqrt{12}=2-\sqrt{3}\] \[\therefore \] \[a+b=2+\sqrt{3}+2-\sqrt{3}=4\] \[ab=(2+\sqrt{3})(2-\sqrt{3})=1\] \[\therefore \] \[{{a}^{3}}+{{b}^{3}}={{(a+b)}^{3}}-3ab\,\,(a+b)\] \[=64-3\times 4=52\]
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