Basic Math Examples

$\sqrt[3]{125 x y^{2}} + \sqrt[3]{27 x^{4} y^{5}}$

Step 1

Rewrite $125 x y^{2}$ as $5^{3} (x y^{2})$ .

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Step 1.1

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

$\sqrt[3]{5^{3} x y^{2}} + \sqrt[3]{27 x^{4} y^{5}}$

Step 1.2

Add parentheses.

$\sqrt[3]{5^{3} (x y^{2})} + \sqrt[3]{27 x^{4} y^{5}}$

Step 2

Pull terms out from under the radical.

$5 \sqrt[3]{x y^{2}} + \sqrt[3]{27 x^{4} y^{5}}$

Step 3

Rewrite $27 x^{4} y^{5}$ as ${(3 x y)}^{3} (x y^{2})$ .

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Step 3.1

Rewrite $27$ as $3^{3}$ .

$5 \sqrt[3]{x y^{2}} + \sqrt[3]{3^{3} x^{4} y^{5}}$

Step 3.2

Factor out $x^{3}$ .

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

Step 3.3

Factor out $y^{3}$ .

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

Step 3.4

Move $x$ .

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

Step 3.5

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

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

Step 3.6

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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