Select the correct answer.

Which expression is equivalent to [tex]\sqrt[3]{27x} + \sqrt[3]{x}[/tex], if [tex]x \neq 0[/tex]?

A. [tex]4 \sqrt[3]{x}[/tex]
B. [tex]\sqrt[3]{28x}[/tex]
C. [tex]3 \sqrt[3]{x}[/tex]
D. [tex]4 \sqrt[3]{x^2}[/tex]



Answer :

To determine the expression equivalent to [tex]\(\sqrt[3]{27 x} + \sqrt[3]{x}\)[/tex], let's analyze it step by step.

Given expression:
[tex]\[ \sqrt[3]{27 x} + \sqrt[3]{x} \][/tex]

First, we recognize that:
[tex]\[ 27 = 3^3 \][/tex]

So, we can rewrite [tex]\(\sqrt[3]{27 x}\)[/tex] as:
[tex]\[ \sqrt[3]{27 x} = \sqrt[3]{3^3 \cdot x} = 3 \sqrt[3]{x} \][/tex]

Now, substituting this back into the original expression, we have:
[tex]\[ \sqrt[3]{27 x} + \sqrt[3]{x} = 3 \sqrt[3]{x} + \sqrt[3]{x} \][/tex]

Next, we can factor out [tex]\(\sqrt[3]{x}\)[/tex] from both terms:
[tex]\[ 3 \sqrt[3]{x} + \sqrt[3]{x} = (3 + 1)\sqrt[3]{x} = 4 \sqrt[3]{x} \][/tex]

Therefore, the expression [tex]\(\sqrt[3]{27 x} + \sqrt[3]{x}\)[/tex] simplifies to:
[tex]\[ 4 \sqrt[3]{x} \][/tex]

By comparing this with the given options, we see the correct choice is:

A. [tex]\(4 \sqrt[3]{x}\)[/tex]

Thus, the correct answer is:
[tex]\[ \boxed{4 \sqrt[3]{x}} \][/tex]