Simplify square root of xy^2z^3+ square root of 9xy^2z^3

$\sqrt{x y^{2} z^{3}} + \sqrt{9 x y^{2} z^{3}}$

Step 1

Simplify each term.

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

Factor out $z^{2}$ .

$\sqrt{x y^{2} (z^{2} z)} + \sqrt{9 x y^{2} z^{3}}$

Move $x$ .

$\sqrt{y^{2} z^{2} x z} + \sqrt{9 x y^{2} z^{3}}$

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

$\sqrt{{(y z)}^{2} x z} + \sqrt{9 x y^{2} z^{3}}$

Add parentheses.

$\sqrt{{(y z)}^{2} (x z)} + \sqrt{9 x y^{2} z^{3}}$

Pull terms out from under the radical.

$y z \sqrt{x z} + \sqrt{9 x y^{2} z^{3}}$

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

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

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

Factor out $z^{2}$ .

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

Move $x$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

$y z \sqrt{x z} + 3 y z \sqrt{x z}$

Step 2

Add $y z \sqrt{x z}$ and $3 y z \sqrt{x z}$ .

$4 y z \sqrt{x z}$