Algebra Examples

$\sqrt{y^{3}} + \sqrt{9 y^{3}} - 3 y \sqrt{y}$

Step 1

Simplify each term.

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Step 1.1

Factor out $y^{2}$ .

$\sqrt{y^{2} y} + \sqrt{9 y^{3}} - 3 y \sqrt{y}$

Step 1.2

Pull terms out from under the radical.

$y \sqrt{y} + \sqrt{9 y^{3}} - 3 y \sqrt{y}$

Step 1.3

Rewrite $9 y^{3}$ as ${(3 y)}^{2} y$ .

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Step 1.3.1

Rewrite $9$ as $3^{2}$ .

$y \sqrt{y} + \sqrt{3^{2} y^{3}} - 3 y \sqrt{y}$

Step 1.3.2

Factor out $y^{2}$ .

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

Step 1.3.3

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

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

Step 1.4

Pull terms out from under the radical.

$y \sqrt{y} + 3 y \sqrt{y} - 3 y \sqrt{y}$

Step 2

Combine the opposite terms in $y \sqrt{y} + 3 y \sqrt{y} - 3 y \sqrt{y}$ .

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Step 2.1

Subtract $3 y \sqrt{y}$ from $3 y \sqrt{y}$ .

$y \sqrt{y} + 0$

Step 2.2

Add $y \sqrt{y}$ and $0$ .

$y \sqrt{y}$