Basic Math Examples

$2 \sqrt[3]{375 y^{8}} + \sqrt[3]{24 y^{8}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $375 y^{8}$ as ${(5 y^{2})}^{3} \cdot (3 y^{2})$ .

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Step 1.1.1

Factor $125$ out of $375$ .

$2 \sqrt[3]{125 (3) y^{8}} + \sqrt[3]{24 y^{8}}$

Step 1.1.2

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

$2 \sqrt[3]{5^{3} \cdot 3 y^{8}} + \sqrt[3]{24 y^{8}}$

Step 1.1.3

Factor out $y^{6}$ .

$2 \sqrt[3]{5^{3} \cdot 3 (y^{6} y^{2})} + \sqrt[3]{24 y^{8}}$

Step 1.1.4

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

$2 \sqrt[3]{5^{3} \cdot 3 ({(y^{2})}^{3} y^{2})} + \sqrt[3]{24 y^{8}}$

Step 1.1.5

Move $3$ .

$2 \sqrt[3]{5^{3} {(y^{2})}^{3} \cdot 3 y^{2}} + \sqrt[3]{24 y^{8}}$

Step 1.1.6

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

$2 \sqrt[3]{{(5 y^{2})}^{3} \cdot 3 y^{2}} + \sqrt[3]{24 y^{8}}$

Step 1.1.7

Add parentheses.

$2 \sqrt[3]{{(5 y^{2})}^{3} \cdot (3 y^{2})} + \sqrt[3]{24 y^{8}}$

Step 1.2

Pull terms out from under the radical.

$2 (5 y^{2} \sqrt[3]{3 y^{2}}) + \sqrt[3]{24 y^{8}}$

Step 1.3

Multiply $5$ by $2$ .

$10 (y^{2} \sqrt[3]{3 y^{2}}) + \sqrt[3]{24 y^{8}}$

Step 1.4

Rewrite $24 y^{8}$ as ${(2 y^{2})}^{3} \cdot (3 y^{2})$ .

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Step 1.4.1

Factor $8$ out of $24$ .

$10 y^{2} \sqrt[3]{3 y^{2}} + \sqrt[3]{8 (3) y^{8}}$

Step 1.4.2

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

$10 y^{2} \sqrt[3]{3 y^{2}} + \sqrt[3]{2^{3} \cdot 3 y^{8}}$

Step 1.4.3

Factor out $y^{6}$ .

$10 y^{2} \sqrt[3]{3 y^{2}} + \sqrt[3]{2^{3} \cdot 3 (y^{6} y^{2})}$

Step 1.4.4

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

$10 y^{2} \sqrt[3]{3 y^{2}} + \sqrt[3]{2^{3} \cdot 3 ({(y^{2})}^{3} y^{2})}$

Step 1.4.5

Move $3$ .

$10 y^{2} \sqrt[3]{3 y^{2}} + \sqrt[3]{2^{3} {(y^{2})}^{3} \cdot 3 y^{2}}$

Step 1.4.6

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

$10 y^{2} \sqrt[3]{3 y^{2}} + \sqrt[3]{{(2 y^{2})}^{3} \cdot 3 y^{2}}$

Step 1.4.7

Add parentheses.

$10 y^{2} \sqrt[3]{3 y^{2}} + \sqrt[3]{{(2 y^{2})}^{3} \cdot (3 y^{2})}$

Step 1.5

Pull terms out from under the radical.

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

Step 2

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

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