Question

question
write the following expression in simplest radical form.
\left(\sqrt3{24s^{5}}\
ight)\left(\sqrt3{3s^{8}}\
ight)

Explanation:

Step1: Multiply the radicals

$\sqrt[3]{24s^5} \times \sqrt[3]{3s^8} = \sqrt[3]{24s^5 \times 3s^8}$

Step2: Simplify the product inside

$\sqrt[3]{(24 \times 3) \times (s^5 \times s^8)} = \sqrt[3]{72s^{13}}$

Step3: Factor into perfect cubes

$\sqrt[3]{8 \times 9 \times s^{12} \times s} = \sqrt[3]{8s^{12}} \times \sqrt[3]{9s}$

Step4: Simplify perfect cube roots

$\sqrt[3]{8s^{12}} = 2s^4$, so $2s^4\sqrt[3]{9s}$

Answer:

$2s^4\sqrt[3]{9s}$