select the correct answer. which expression is equivalent to $sqrt3{27x}+sqrt3{x}$, if $x\neq0$?\na…

select the correct answer. which expression is equivalent to $sqrt3{27x}+sqrt3{x}$, if $x\neq0$?\na. $4sqrt3{x}$\nb. $sqrt3{28x}$\nc. $3sqrt3{x}$\nd. $4sqrt3{x^{2}}$

select the correct answer. which expression is equivalent to $sqrt3{27x}+sqrt3{x}$, if $x\neq0$?\na. $4sqrt3{x}$\nb. $sqrt3{28x}$\nc. $3sqrt3{x}$\nd. $4sqrt3{x^{2}}$

Answer

Explanation:

Step1: Simplify $\sqrt[3]{27x}$

We know that $27 = 3^3$, so $\sqrt[3]{27x}=\sqrt[3]{3^3\times x}=3\sqrt[3]{x}$.

Step2: Combine like - terms

The original expression is $\sqrt[3]{27x}+\sqrt[3]{x}$. Substituting the simplified form of $\sqrt[3]{27x}$, we get $3\sqrt[3]{x}+\sqrt[3]{x}=(3 + 1)\sqrt[3]{x}=4\sqrt[3]{x}$.

Answer:

A. $4\sqrt[3]{x}$