Simplify the Radical Expression 3 cube root of 5y^3*2 cube root of 50y^4

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

Step 1

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $2$ by $3$ .

$6 y \sqrt[3]{5} \sqrt[3]{50 y^{4}}$

Step 4

Rewrite $50 y^{4}$ as $y^{3} \cdot (50 y)$ .

Factor out $y^{3}$ .

$6 y \sqrt[3]{5} \sqrt[3]{50 (y^{3} y)}$

Reorder $50$ and $y^{3}$ .

$6 y \sqrt[3]{5} \sqrt[3]{y^{3} \cdot 50 y}$

Add parentheses.

$6 y \sqrt[3]{5} \sqrt[3]{y^{3} \cdot (50 y)}$

$6 y \sqrt[3]{5} \sqrt[3]{y^{3} \cdot (50 y)}$

Step 5

Pull terms out from under the radical.

$6 y \sqrt[3]{5} (y \sqrt[3]{50 y})$

Step 6

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$6 (y \cdot y) \sqrt[3]{5} \sqrt[3]{50 y}$

Multiply $y$ by $y$ .

$6 y^{2} \sqrt[3]{5} \sqrt[3]{50 y}$

$6 y^{2} \sqrt[3]{5} \sqrt[3]{50 y}$

Step 7

Multiply $6 y^{2} \sqrt[3]{5} \sqrt[3]{50 y}$ .

Combine using the product rule for radicals.

$6 y^{2} \sqrt[3]{50 y \cdot 5}$

Multiply $5$ by $50$ .

$6 y^{2} \sqrt[3]{250 y}$

$6 y^{2} \sqrt[3]{250 y}$

Step 8

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

Factor $125$ out of $250$ .

$6 y^{2} \sqrt[3]{125 (2) y}$

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

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

Add parentheses.

$6 y^{2} \sqrt[3]{5^{3} \cdot (2 y)}$

$6 y^{2} \sqrt[3]{5^{3} \cdot (2 y)}$

Step 9

Pull terms out from under the radical.

$6 y^{2} (5 \sqrt[3]{2 y})$

Step 10

Multiply $5$ by $6$ .

$30 y^{2} \sqrt[3]{2 y}$

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