Algebra Examples

$5 x \sqrt[3]{25 x^{4} y^{2}} + 5 y \sqrt[4]{4 x^{2} y^{4}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $25 x^{4} y^{2}$ as $x^{3} \cdot (25 x y^{2})$ .

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Step 1.1.1

Factor out $x^{3}$ .

$5 x \sqrt[3]{25 (x^{3} x) y^{2}} + 5 y \sqrt[4]{4 x^{2} y^{4}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.1.2

Reorder $25$ and $x^{3}$ .

$5 x \sqrt[3]{x^{3} \cdot 25 x y^{2}} + 5 y \sqrt[4]{4 x^{2} y^{4}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.1.3

Add parentheses.

$5 x \sqrt[3]{x^{3} \cdot 25 (x y^{2})} + 5 y \sqrt[4]{4 x^{2} y^{4}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.1.4

Add parentheses.

$5 x \sqrt[3]{x^{3} \cdot (25 x y^{2})} + 5 y \sqrt[4]{4 x^{2} y^{4}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.2

Pull terms out from under the radical.

$5 x (x \sqrt[3]{25 x y^{2}}) + 5 y \sqrt[4]{4 x^{2} y^{4}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 1.3.1

Move $x$ .

$5 (x \cdot x) \sqrt[3]{25 x y^{2}} + 5 y \sqrt[4]{4 x^{2} y^{4}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.3.2

Multiply $x$ by $x$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y \sqrt[4]{4 x^{2} y^{4}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.4

Rewrite $4 x^{2} y^{4}$ as $y^{4} \cdot (4 x^{2})$ .

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Step 1.4.1

Move $x^{2}$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y \sqrt[4]{4 y^{4} x^{2}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.4.2

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

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y \sqrt[4]{y^{4} \cdot 4 x^{2}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.4.3

Add parentheses.

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y \sqrt[4]{y^{4} \cdot (4 x^{2})} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.5

Pull terms out from under the radical.

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y (y \sqrt[4]{4 x^{2}}) - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.6

Multiply $y$ by $y$ by adding the exponents.

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Step 1.6.1

Move $y$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 (y \cdot y) \sqrt[4]{4 x^{2}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.6.2

Multiply $y$ by $y$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt[4]{4 x^{2}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.7

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt[4]{{(2 x)}^{2}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.8

Rewrite $\sqrt[4]{{(2 x)}^{2}}$ as $\sqrt{\sqrt{{(2 x)}^{2}}}$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{\sqrt{{(2 x)}^{2}}} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.9

Pull terms out from under the radical, assuming positive real numbers.

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x \sqrt[3]{25 x^{4} y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.10

Rewrite $25 x^{4} y^{2}$ as $x^{3} \cdot (25 x y^{2})$ .

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Step 1.10.1

Factor out $x^{3}$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x \sqrt[3]{25 (x^{3} x) y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.10.2

Reorder $25$ and $x^{3}$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x \sqrt[3]{x^{3} \cdot 25 x y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.10.3

Add parentheses.

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x \sqrt[3]{x^{3} \cdot 25 (x y^{2})} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.10.4

Add parentheses.

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x \sqrt[3]{x^{3} \cdot (25 x y^{2})} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.11

Pull terms out from under the radical.

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x (x \sqrt[3]{25 x y^{2}}) + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.12

Multiply $x$ by $x$ by adding the exponents.

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Step 1.12.1

Move $x$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 (x \cdot x) \sqrt[3]{25 x y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.12.2

Multiply $x$ by $x$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x^{2} \sqrt[3]{25 x y^{2}} + 6 x \sqrt[3]{25 x^{4} y^{2}}$

Step 1.13

Rewrite $25 x^{4} y^{2}$ as $x^{3} \cdot (25 x y^{2})$ .

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Step 1.13.1

Factor out $x^{3}$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x^{2} \sqrt[3]{25 x y^{2}} + 6 x \sqrt[3]{25 (x^{3} x) y^{2}}$

Step 1.13.2

Reorder $25$ and $x^{3}$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x^{2} \sqrt[3]{25 x y^{2}} + 6 x \sqrt[3]{x^{3} \cdot 25 x y^{2}}$

Step 1.13.3

Add parentheses.

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x^{2} \sqrt[3]{25 x y^{2}} + 6 x \sqrt[3]{x^{3} \cdot 25 (x y^{2})}$

Step 1.13.4

Add parentheses.

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x^{2} \sqrt[3]{25 x y^{2}} + 6 x \sqrt[3]{x^{3} \cdot (25 x y^{2})}$

Step 1.14

Pull terms out from under the radical.

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x^{2} \sqrt[3]{25 x y^{2}} + 6 x (x \sqrt[3]{25 x y^{2}})$

Step 1.15

Multiply $x$ by $x$ by adding the exponents.

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Step 1.15.1

Move $x$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x^{2} \sqrt[3]{25 x y^{2}} + 6 (x \cdot x) \sqrt[3]{25 x y^{2}}$

Step 1.15.2

Multiply $x$ by $x$ .

$5 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} - 8 x^{2} \sqrt[3]{25 x y^{2}} + 6 x^{2} \sqrt[3]{25 x y^{2}}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $8 x^{2} \sqrt[3]{25 x y^{2}}$ from $5 x^{2} \sqrt[3]{25 x y^{2}}$ .

$- 3 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x} + 6 x^{2} \sqrt[3]{25 x y^{2}}$

Step 2.2

Add $- 3 x^{2} \sqrt[3]{25 x y^{2}}$ and $6 x^{2} \sqrt[3]{25 x y^{2}}$ .

$3 x^{2} \sqrt[3]{25 x y^{2}} + 5 y^{2} \sqrt{2 x}$