Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor out $y^{2}$ .

$\sqrt{x^{2} (y^{2} y)} + 2 \sqrt{x^{3} y^{4}} + x y \sqrt{y}$

Step 1.1.2

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

$\sqrt{{(x y)}^{2} y} + 2 \sqrt{x^{3} y^{4}} + x y \sqrt{y}$

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

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

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Step 1.3.1

Factor out $x^{2}$ .

$x y \sqrt{y} + 2 \sqrt{x^{2} x y^{4}} + x y \sqrt{y}$

Step 1.3.2

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

$x y \sqrt{y} + 2 \sqrt{x^{2} x {(y^{2})}^{2}} + x y \sqrt{y}$

Step 1.3.3

Move $x$ .

$x y \sqrt{y} + 2 \sqrt{x^{2} {(y^{2})}^{2} x} + x y \sqrt{y}$

Step 1.3.4

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

$x y \sqrt{y} + 2 \sqrt{{(x y^{2})}^{2} x} + x y \sqrt{y}$

Step 1.4

Pull terms out from under the radical.

$x y \sqrt{y} + 2 x y^{2} \sqrt{x} + x y \sqrt{y}$

Step 2

Add $x y \sqrt{y}$ and $x y \sqrt{y}$ .

$2 x y \sqrt{y} + 2 x y^{2} \sqrt{x}$