Precalculus Examples

$\sqrt[3]{128 x y^{3}} + y \sqrt[3]{16 x}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $128 x y^{3}$ as ${(4 y)}^{3} \cdot (2 x)$ .

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Step 1.1.1

Factor $64$ out of $128$ .

$\sqrt[3]{64 (2) x y^{3}} + y \sqrt[3]{16 x}$

Step 1.1.2

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{4^{3} \cdot 2 x y^{3}} + y \sqrt[3]{16 x}$

Step 1.1.3

Move $x$ .

$\sqrt[3]{4^{3} \cdot 2 y^{3} x} + y \sqrt[3]{16 x}$

Step 1.1.4

Move $2$ .

$\sqrt[3]{4^{3} y^{3} \cdot 2 x} + y \sqrt[3]{16 x}$

Step 1.1.5

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

$\sqrt[3]{{(4 y)}^{3} \cdot 2 x} + y \sqrt[3]{16 x}$

Step 1.1.6

Add parentheses.

$\sqrt[3]{{(4 y)}^{3} \cdot (2 x)} + y \sqrt[3]{16 x}$

Step 1.2

Pull terms out from under the radical.

$4 y \sqrt[3]{2 x} + y \sqrt[3]{16 x}$

Step 1.3

Rewrite $16 x$ as $2^{3} \cdot (2 x)$ .

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Step 1.3.1

Factor $8$ out of $16$ .

$4 y \sqrt[3]{2 x} + y \sqrt[3]{8 (2) x}$

Step 1.3.2

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

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

Step 1.3.3

Add parentheses.

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Rewrite using the commutative property of multiplication.

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

Step 2

Add $4 y \sqrt[3]{2 x}$ and $2 y \sqrt[3]{2 x}$ .

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