Question

The value of $\sqrt[3]{324}+\sqrt[3]{381}-\sqrt[3]{3192}$, is

• A. $\sqrt[3]{33}$
• B. $\sqrt{3}$
• C. $3$
• D. None of these

Answer 1

The correct option is A $\sqrt[3]{33}$

$\sqrt[3]{324}+\sqrt[3]{381}-\sqrt[3]{3192}=\sqrt[3]{38\ast 3}+\sqrt[3]{327\ast 3}-\sqrt[3]{364\ast 3}=\sqrt[3]{32^3\ast 3}+\sqrt[3]{33^3\ast 3}-\sqrt[3]{34^3\ast 3}=2\sqrt[3]{33}+3\sqrt[3]{33}-4\sqrt[3]{33}=\sqrt[3]{33}$