Question

simplify the expression. assume that all variables represent positive numbers.
\sqrt3{10a^{3}b^{2}} \cdot \sqrt3{25a^{2}b} = \square

Explanation:

Step1: Combine cube roots

$\sqrt[3]{10a^3b^2 \cdot 25a^2b}$

Step2: Multiply inside the root

$\sqrt[3]{(10 \cdot 25) \cdot (a^3 \cdot a^2) \cdot (b^2 \cdot b)}$
$\sqrt[3]{250a^5b^3}$

Step3: Factor into perfect cubes

$\sqrt[3]{125 \cdot 2 \cdot a^3 \cdot a^2 \cdot b^3}$
$\sqrt[3]{125a^3b^3 \cdot 2a^2}$

Step4: Extract perfect cubes

$5ab\sqrt[3]{2a^2}$

Answer:

$5ab\sqrt[3]{2a^2}$