A) \[\sqrt[3]{3}-1\]
B) \[\sqrt[3]{3}+1\]
C) \[\sqrt[3]{9}+1\]
D) \[\sqrt[3]{9}-1\]
Correct Answer: B
Solution :
\[\sqrt[3]{9}-\sqrt[3]{3}+1={{(3)}^{\frac{2}{3}}}-{{(3)}^{\frac{1}{3}}}+{{(1)}^{\frac{2}{3}}}\] \[\therefore \]\[(\sqrt[3]{3}+1)(\sqrt[3]{9}-\sqrt[3]{3}+1)={{({{3}^{\frac{1}{3}}})}^{3}}+1=3+1=4\] \[[\because {{a}^{3}}+{{b}^{3}}=(a+b)({{a}^{2}}-ab+{{b}^{2}})]\] \[\therefore \] Rationalising factor \[=\sqrt[3]{3}+1\]
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