Algebra Examples

$\sqrt[3]{27 x y^{2}} - \sqrt[3]{64 x^{4} y^{5}}$

Step 1

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

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Step 1.1

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

$\sqrt[3]{3^{3} x y^{2}} - \sqrt[3]{64 x^{4} y^{5}}$

Step 1.2

Add parentheses.

$\sqrt[3]{3^{3} (x y^{2})} - \sqrt[3]{64 x^{4} y^{5}}$

Step 2

Pull terms out from under the radical.

$3 \sqrt[3]{x y^{2}} - \sqrt[3]{64 x^{4} y^{5}}$

Step 3

Rewrite $64 x^{4} y^{5}$ as ${(4 x y)}^{3} (x y^{2})$ .

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Step 3.1

Rewrite $64$ as $4^{3}$ .

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

Step 3.2

Factor out $x^{3}$ .

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

Step 3.3

Factor out $y^{3}$ .

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

Step 3.4

Move $x$ .

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

Step 3.5

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

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

Step 3.6

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $4$ by $- 1$ .

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