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Simplify y square root of z^2y^3+2z square root of y^5

$y \sqrt{z^{2} y^{3}} + 2 z \sqrt{y^{5}}$

Step 1

Simplify each term.

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

Factor out $y^{2}$ .

$y \sqrt{z^{2} (y^{2} y)} + 2 z \sqrt{y^{5}}$

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

$y \sqrt{{(z y)}^{2} y} + 2 z \sqrt{y^{5}}$

$y \sqrt{{(z y)}^{2} y} + 2 z \sqrt{y^{5}}$

Pull terms out from under the radical.

$y (z y \sqrt{y}) + 2 z \sqrt{y^{5}}$

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

Move $y$ .

$y \cdot y (z \sqrt{y}) + 2 z \sqrt{y^{5}}$

Multiply $y$ by $y$ .

$y^{2} (z \sqrt{y}) + 2 z \sqrt{y^{5}}$

$y^{2} (z \sqrt{y}) + 2 z \sqrt{y^{5}}$

Rewrite $y^{5}$ as ${(y^{2})}^{2} y$ .

Factor out $y^{4}$ .

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

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

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

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

Pull terms out from under the radical.

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

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

Step 2

Simplify by adding terms.

Move $z$ .

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

Add $y^{2} z \sqrt{y}$ and $2 y^{2} z \sqrt{y}$ .

$3 y^{2} z \sqrt{y}$

$3 y^{2} z \sqrt{y}$

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