3\\sqrt3{162}+3\\sqrt3{81}-4\\sqrt3{24}\na) 9\\sqrt3{6}+17\\sqrt3{3}\nb) 9\\sqrt3{6}\nc) 9\\sqrt3{6}+9\\sqrt3…

3\\sqrt3{162}+3\\sqrt3{81}-4\\sqrt3{24}\na) 9\\sqrt3{6}+17\\sqrt3{3}\nb) 9\\sqrt3{6}\nc) 9\\sqrt3{6}+9\\sqrt3{3}\nd) 9\\sqrt3{6}+\\sqrt3{3}\n○a\n○b\n○c\n○d

3\\sqrt3{162}+3\\sqrt3{81}-4\\sqrt3{24}\na) 9\\sqrt3{6}+17\\sqrt3{3}\nb) 9\\sqrt3{6}\nc) 9\\sqrt3{6}+9\\sqrt3{3}\nd) 9\\sqrt3{6}+\\sqrt3{3}\n○a\n○b\n○c\n○d

Answer

Explanation:

Step1: Simplify cube - roots

First, simplify $\sqrt[3]{162}$, $\sqrt[3]{81}$, and $\sqrt[3]{24}$. We know that $162 = 2\times3^4= 2\times3^3\times3$, so $\sqrt[3]{162}=\sqrt[3]{2\times3^3\times3}=3\sqrt[3]{6}$. $81 = 3^4 = 3^3\times3$, so $\sqrt[3]{81}=\sqrt[3]{3^3\times3}=3\sqrt[3]{3}$. $24=2^3\times3$, so $\sqrt[3]{24}=\sqrt[3]{2^3\times3}=2\sqrt[3]{3}$.

Step2: Substitute into the original expression

The original expression $3\sqrt[3]{162}+3\sqrt[3]{81}-4\sqrt[3]{24}$ becomes: $3\times3\sqrt[3]{6}+3\times3\sqrt[3]{3}-4\times2\sqrt[3]{3}$. $9\sqrt[3]{6}+9\sqrt[3]{3}-8\sqrt[3]{3}$.

Step3: Combine like - terms

Combine the terms with $\sqrt[3]{3}$: $9\sqrt[3]{6}+(9 - 8)\sqrt[3]{3}=9\sqrt[3]{6}+\sqrt[3]{3}$.

Answer:

D. $9\sqrt[3]{6}+\sqrt[3]{3}$