Finite Math Examples

$- 9 x y \sqrt[4]{4 y^{3}} + 9 \sqrt{14 x^{3} y^{2}} + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{14 x^{3} y^{2}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $14 x^{3} y^{2}$ as ${(x y)}^{2} \cdot (14 x)$ .

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Step 1.1.1

Factor out $x^{2}$ .

$- 9 x y \sqrt[4]{4 y^{3}} + 9 \sqrt{14 (x^{2} x) y^{2}} + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{14 x^{3} y^{2}}$

Step 1.1.2

Move $x$ .

$- 9 x y \sqrt[4]{4 y^{3}} + 9 \sqrt{14 (x^{2}) y^{2} x} + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{14 x^{3} y^{2}}$

Step 1.1.3

Move $14$ .

$- 9 x y \sqrt[4]{4 y^{3}} + 9 \sqrt{(x^{2}) y^{2} \cdot 14 x} + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{14 x^{3} y^{2}}$

Step 1.1.4

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

$- 9 x y \sqrt[4]{4 y^{3}} + 9 \sqrt{{(x y)}^{2} \cdot 14 x} + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{14 x^{3} y^{2}}$

Step 1.1.5

Add parentheses.

$- 9 x y \sqrt[4]{4 y^{3}} + 9 \sqrt{{(x y)}^{2} \cdot (14 x)} + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{14 x^{3} y^{2}}$

Step 1.2

Pull terms out from under the radical.

$- 9 x y \sqrt[4]{4 y^{3}} + 9 (x y \sqrt{14 x}) + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{14 x^{3} y^{2}}$

Step 1.3

Rewrite $14 x^{3} y^{2}$ as ${(x y)}^{2} \cdot (14 x)$ .

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Step 1.3.1

Factor out $x^{2}$ .

$- 9 x y \sqrt[4]{4 y^{3}} + 9 x y \sqrt{14 x} + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{14 (x^{2} x) y^{2}}$

Step 1.3.2

Move $x$ .

$- 9 x y \sqrt[4]{4 y^{3}} + 9 x y \sqrt{14 x} + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{14 (x^{2}) y^{2} x}$

Step 1.3.3

Move $14$ .

$- 9 x y \sqrt[4]{4 y^{3}} + 9 x y \sqrt{14 x} + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{(x^{2}) y^{2} \cdot 14 x}$

Step 1.3.4

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

$- 9 x y \sqrt[4]{4 y^{3}} + 9 x y \sqrt{14 x} + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{{(x y)}^{2} \cdot 14 x}$

Step 1.3.5

Add parentheses.

$- 9 x y \sqrt[4]{4 y^{3}} + 9 x y \sqrt{14 x} + 5 x y \sqrt[4]{4 y^{3}} + 3 \sqrt{{(x y)}^{2} \cdot (14 x)}$

Step 1.4

Pull terms out from under the radical.

$- 9 x y \sqrt[4]{4 y^{3}} + 9 x y \sqrt{14 x} + 5 x y \sqrt[4]{4 y^{3}} + 3 x y \sqrt{14 x}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 9 x y \sqrt[4]{4 y^{3}}$ and $5 x y \sqrt[4]{4 y^{3}}$ .

$- 4 x y \sqrt[4]{4 y^{3}} + 9 x y \sqrt{14 x} + 3 x y \sqrt{14 x}$

Step 2.2

Add $9 x y \sqrt{14 x}$ and $3 x y \sqrt{14 x}$ .

$- 4 x y \sqrt[4]{4 y^{3}} + 12 x y \sqrt{14 x}$