Question

select the correct answer.

which expression is equivalent to \\(\sqrt3{27x} + \sqrt3{x}\\) if \\(x \
eq 0\\)?

\\(4\sqrt3{x}\\)

\\(\sqrt3{28x}\\)

\\(3\sqrt3{x}\\)

\\(4\sqrt3{x^2}\\)

Explanation:

Simplify the first radical term

$$ \sqrt[3]{27x} = \sqrt[3]{27} \cdot \sqrt[3]{x} = 3\sqrt[3]{x} $$

Combine the like radical terms

$$ 3\sqrt[3]{x} + \sqrt[3]{x} = (3 + 1)\sqrt[3]{x} = 4\sqrt[3]{x} $$

Answer:

• (A) \(4\sqrt[3]{x}\) (Correct answer)
• (B) \(\sqrt[3]{28x}\)
• (C) \(3\sqrt[3]{x}\)
• (D) \(4\sqrt[3]{x^2}\)