$2\sqrt[3]{4} \cdot 2\sqrt[3]{2}$ $\newline$ What is the value of the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $2\sqrt[3]{6}$ $\newline$ (B) $4\sqrt[6]{8}$ $\newline$ (C) $8$ $\newline$ (D) $16$

Full solution

2\sqrt[3]{4} \cdot 2\sqrt[3]{2}

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What is the value of the given expression?

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Choose

1

answer:

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(A)

2\sqrt[3]{6}

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(B)

4\sqrt[6]{8}

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(C)

8

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(D)

16

Identify Properties: Identify the properties of radicals and multiplication. $\newline$ When multiplying two numbers with the same radical (in this case, cube roots), you can multiply the numbers under the radical first and then take the cube root of the product.
Multiply Numbers: Multiply the numbers under the cube root. $\newline$ We have $2\sqrt[3]{4} \times 2\sqrt[3]{2}$ , which means we multiply $4$ and $2$ under the cube root, while also multiplying the coefficients $2$ and $2$ outside the cube root.
Perform Multiplication: Perform the multiplication. $\newline$ Multiplying the coefficients gives us $2 \times 2 = 4$ . Multiplying the numbers under the cube root gives us $4 \times 2 = 8$ . So we have $4\sqrt[3]{8}$ .
Simplify Expression: Simplify the expression if possible. $\newline$ The cube root of $8$ is $2$ , so we can simplify $4\sqrt[3]{8}$ to $4 \times 2$ .
Calculate Final Result: Calculate the final result. $\newline$ Multiplying $4$ by $2$ gives us $8$ . So the final answer is $8$ .