Question

write the following product in simplest form.
\sqrt3{81} \cdot \sqrt3{45}
\sqrt3{81} \cdot \sqrt3{45} = \square
(simplify your answer. type an exact answer using radicals as ne

Explanation:

Step1: Combine cube roots

$\sqrt[3]{81} \cdot \sqrt[3]{45} = \sqrt[3]{81 \times 45}$

Step2: Factor the product inside

$81 \times 45 = 3^4 \times 3^2 \times 5 = 3^6 \times 5$

Step3: Simplify the cube root

$\sqrt[3]{3^6 \times 5} = \sqrt[3]{3^6} \cdot \sqrt[3]{5} = 3^2 \cdot \sqrt[3]{5}$

Step4: Calculate the integer term

$3^2 = 9$

Answer:

$9\sqrt[3]{5}$