Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor out $z^{6}$ .

$2 y \sqrt[3]{z^{6} z^{2}} + 3 z^{2} \sqrt[3]{8 y^{3} z^{2}}$

Step 1.1.2

Rewrite $z^{6}$ as ${(z^{2})}^{3}$ .

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

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

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Multiply $2$ by $3$ .

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

Step 2

Add $2 y z^{2} \sqrt[3]{z^{2}}$ and $6 z^{2} (y \sqrt[3]{z^{2}})$ .

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Step 2.1

Move $z^{2}$ .

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

Step 2.2

Add $2 y z^{2} \sqrt[3]{z^{2}}$ and $6 y z^{2} \sqrt[3]{z^{2}}$ .

$8 y z^{2} \sqrt[3]{z^{2}}$