Finite Math Examples

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

Step 1

Apply the distributive property.

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

Step 2

Multiply $\sqrt[3]{4 x y} \sqrt[3]{2 x^{2}}$ .

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Step 2.1

Combine using the product rule for radicals.

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

Step 2.2

Multiply $2$ by $4$ .

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

Step 2.3

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 2.3.1

Move $x^{2}$ .

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

Step 2.3.2

Multiply $x^{2}$ by $x$ .

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Step 2.3.2.1

Raise $x$ to the power of $1$ .

$\sqrt[3]{8 (x^{2} x^{1}) y} + \sqrt[3]{4 x y} \sqrt[3]{y^{2}}$

Step 2.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[3]{8 x^{2 + 1} y} + \sqrt[3]{4 x y} \sqrt[3]{y^{2}}$

Step 2.3.3

Add $2$ and $1$ .

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

Step 3

Multiply $\sqrt[3]{4 x y} \sqrt[3]{y^{2}}$ .

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Step 3.1

Combine using the product rule for radicals.

$\sqrt[3]{8 x^{3} y} + \sqrt[3]{4 x y \cdot y^{2}}$

Step 3.2

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 3.2.1

Move $y^{2}$ .

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

Step 3.2.2

Multiply $y^{2}$ by $y$ .

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Step 3.2.2.1

Raise $y$ to the power of $1$ .

$\sqrt[3]{8 x^{3} y} + \sqrt[3]{4 x (y^{2} y^{1})}$

Step 3.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[3]{8 x^{3} y} + \sqrt[3]{4 x y^{2 + 1}}$

Step 3.2.3

Add $2$ and $1$ .

$\sqrt[3]{8 x^{3} y} + \sqrt[3]{4 x y^{3}}$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

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

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

Step 4.2

Pull terms out from under the radical.

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

Step 4.3

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

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Step 4.3.1

Move $x$ .

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

Step 4.3.2

Reorder $4$ and $y^{3}$ .

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

Step 4.3.3

Add parentheses.

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

Step 4.4

Pull terms out from under the radical.

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