Question

write the product in its simplest form.
\sqrt3{3} \cdot \sqrt3{8}
\sqrt3{3} \cdot \sqrt3{8} = \square
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Use the property of radicals $\sqrt[3]{a}\cdot\sqrt[3]{b}=\sqrt[3]{ab}$

$\sqrt[3]{3}\cdot\sqrt[3]{8}=\sqrt[3]{3\times8}$

Step2: Calculate the product inside the cube root

$3\times8 = 24$, so we have $\sqrt[3]{24}$

Step3: Simplify $\sqrt[3]{24}$ by factoring 24

$24 = 8\times3$, and $\sqrt[3]{8}=2$, so $\sqrt[3]{24}=\sqrt[3]{8\times3}=\sqrt[3]{8}\cdot\sqrt[3]{3}=2\sqrt[3]{3}$

Answer:

$2\sqrt[3]{3}$