Simplify the Radical Expression 7 cube root of 8x^2y+2 cube root of 27x^5y^4

$7 \sqrt[3]{8 x^{2} y} + 2 \sqrt[3]{27 x^{5} y^{4}}$

Step 1

Rewrite $8 x^{2} y$ as $2^{3} (x^{2} y)$ .

Rewrite $8$ as $2^{3}$ .

$7 \sqrt[3]{2^{3} x^{2} y} + 2 \sqrt[3]{27 x^{5} y^{4}}$

Add parentheses.

$7 \sqrt[3]{2^{3} (x^{2} y)} + 2 \sqrt[3]{27 x^{5} y^{4}}$

Step 2

Pull terms out from under the radical.

$7 (2 \sqrt[3]{x^{2} y}) + 2 \sqrt[3]{27 x^{5} y^{4}}$

Step 3

Multiply $2$ by $7$ .

$14 \sqrt[3]{x^{2} y} + 2 \sqrt[3]{27 x^{5} y^{4}}$

Step 4

Rewrite $27 x^{5} y^{4}$ as ${(3 x y)}^{3} (x^{2} y)$ .

Rewrite $27$ as $3^{3}$ .

$14 \sqrt[3]{x^{2} y} + 2 \sqrt[3]{3^{3} x^{5} y^{4}}$

Factor out $x^{3}$ .

$14 \sqrt[3]{x^{2} y} + 2 \sqrt[3]{3^{3} (x^{3} x^{2}) y^{4}}$

Factor out $y^{3}$ .

$14 \sqrt[3]{x^{2} y} + 2 \sqrt[3]{3^{3} (x^{3} x^{2}) (y^{3} y)}$

Move $x^{2}$ .

$14 \sqrt[3]{x^{2} y} + 2 \sqrt[3]{3^{3} (x^{3}) y^{3} x^{2} y}$

Rewrite $3^{3} (x^{3}) y^{3}$ as ${(3 x y)}^{3}$ .

$14 \sqrt[3]{x^{2} y} + 2 \sqrt[3]{{(3 x y)}^{3} x^{2} y}$

Add parentheses.

$14 \sqrt[3]{x^{2} y} + 2 \sqrt[3]{{(3 x y)}^{3} (x^{2} y)}$

Step 5

Pull terms out from under the radical.

$14 \sqrt[3]{x^{2} y} + 2 (3 x y \sqrt[3]{x^{2} y})$

Step 6

Multiply $3$ by $2$ .

$14 \sqrt[3]{x^{2} y} + 6 x y \sqrt[3]{x^{2} y}$