Simplify 4( cube root of 5y^3)(2 cube root of 50y)

$4 (\sqrt[3]{5 y^{3}}) (2 \sqrt[3]{50 y})$

Step 1

Reorder $5$ and $y^{3}$ .

$4 \sqrt[3]{y^{3} \cdot 5} (2 \sqrt[3]{50 y})$

Step 2

Pull terms out from under the radical.

$4 (y \sqrt[3]{5}) (2 \sqrt[3]{50 y})$

Step 3

Multiply $4 y \sqrt[3]{5} (2 \sqrt[3]{50 y})$ .

Multiply $2$ by $4$ .

$8 y \sqrt[3]{5} \sqrt[3]{50 y}$

Combine using the product rule for radicals.

$8 y \sqrt[3]{50 y \cdot 5}$

Multiply $5$ by $50$ .

$8 y \sqrt[3]{250 y}$

$8 y \sqrt[3]{250 y}$

Step 4

Rewrite $250 y$ as $5^{3} \cdot (2 y)$ .

Factor $125$ out of $250$ .

$8 y \sqrt[3]{125 (2) y}$

Rewrite $125$ as $5^{3}$ .

$8 y \sqrt[3]{5^{3} \cdot 2 y}$

Add parentheses.

$8 y \sqrt[3]{5^{3} \cdot (2 y)}$

$8 y \sqrt[3]{5^{3} \cdot (2 y)}$

Step 5

Pull terms out from under the radical.

$8 y (5 \sqrt[3]{2 y})$

Step 6

Multiply $5$ by $8$ .

$40 y \sqrt[3]{2 y}$

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