which of the following is a like radical to $sqrt3{6x^{2}}$?\n$x(sqrt3{6x})$\n$6(sqrt3{x^{2}})$\n$4(sqrt3{6x^…
which of the following is a like radical to $sqrt3{6x^{2}}$?\n$x(sqrt3{6x})$\n$6(sqrt3{x^{2}})$\n$4(sqrt3{6x^{2}})$\n$x(sqrt3{6})$
Answer
Explanation:
Step1: Recall like - radical definition
Like radicals have the same index and the same radicand. The given radical is $\sqrt[3]{6x^{2}}$, which has an index of 3.
Step2: Analyze each option
- Option 1: $x\sqrt[3]{6x}=\sqrt[3]{x^{3}}\cdot\sqrt[3]{6x}=\sqrt[3]{6x^{4}}$, different radicand.
- Option 2: $6\sqrt[3]{x^{2}}$, different radicand.
- Option 3: $4\sqrt[3]{6x^{2}}$, has the same index (3) and the same radicand ($6x^{2}$) as $\sqrt[3]{6x^{2}}$.
- Option 4: $x\sqrt[3]{6}=\sqrt[3]{x^{3}}\cdot\sqrt[3]{6}=\sqrt[3]{6x^{3}}$, different radicand.
Answer:
C. $4\sqrt[3]{6x^{2}}$