Pre-Algebra Examples

$\sqrt[3]{250 x y^{3}} + 5 \sqrt[3]{2 x y^{3}} + y \sqrt[3]{16 x}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $125$ out of $250$ .

$\sqrt[3]{125 (2) x y^{3}} + 5 \sqrt[3]{2 x y^{3}} + y \sqrt[3]{16 x}$

Step 1.1.2

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

$\sqrt[3]{5^{3} \cdot 2 x y^{3}} + 5 \sqrt[3]{2 x y^{3}} + y \sqrt[3]{16 x}$

Step 1.1.3

Move $x$ .

$\sqrt[3]{5^{3} \cdot 2 y^{3} x} + 5 \sqrt[3]{2 x y^{3}} + y \sqrt[3]{16 x}$

Step 1.1.4

Move $2$ .

$\sqrt[3]{5^{3} y^{3} \cdot 2 x} + 5 \sqrt[3]{2 x y^{3}} + y \sqrt[3]{16 x}$

Step 1.1.5

Rewrite $5^{3} y^{3}$ as ${(5 y)}^{3}$ .

$\sqrt[3]{{(5 y)}^{3} \cdot 2 x} + 5 \sqrt[3]{2 x y^{3}} + y \sqrt[3]{16 x}$

Step 1.1.6

Add parentheses.

$\sqrt[3]{{(5 y)}^{3} \cdot (2 x)} + 5 \sqrt[3]{2 x y^{3}} + y \sqrt[3]{16 x}$

Step 1.2

Pull terms out from under the radical.

$5 y \sqrt[3]{2 x} + 5 \sqrt[3]{2 x y^{3}} + y \sqrt[3]{16 x}$

Step 1.3

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

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Step 1.3.1

Move $x$ .

$5 y \sqrt[3]{2 x} + 5 \sqrt[3]{2 y^{3} x} + y \sqrt[3]{16 x}$

Step 1.3.2

Reorder $2$ and $y^{3}$ .

$5 y \sqrt[3]{2 x} + 5 \sqrt[3]{y^{3} \cdot 2 x} + y \sqrt[3]{16 x}$

Step 1.3.3

Add parentheses.

$5 y \sqrt[3]{2 x} + 5 \sqrt[3]{y^{3} \cdot (2 x)} + y \sqrt[3]{16 x}$

Step 1.4

Pull terms out from under the radical.

$5 y \sqrt[3]{2 x} + 5 (y \sqrt[3]{2 x}) + y \sqrt[3]{16 x}$

Step 1.5

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

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Step 1.5.1

Factor $8$ out of $16$ .

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

Step 1.5.2

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

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

Step 1.5.3

Add parentheses.

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

Step 1.6

Pull terms out from under the radical.

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

Step 1.7

Rewrite using the commutative property of multiplication.

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

Step 2

Simplify by adding terms.

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Step 2.1

Add $5 y \sqrt[3]{2 x}$ and $5 y \sqrt[3]{2 x}$ .

$10 y \sqrt[3]{2 x} + 2 y \sqrt[3]{2 x}$

Step 2.2

Add $10 y \sqrt[3]{2 x}$ and $2 y \sqrt[3]{2 x}$ .

$12 y \sqrt[3]{2 x}$