Simplify -2x^2 square root of 3x^3y^2z^5

$- 2 x^{2} \sqrt{3 x^{3} y^{2} z^{5}}$

Rewrite $3 x^{3} y^{2} z^{5}$ as ${(x y z^{2})}^{2} \cdot (3 x z)$ .

Factor out $x^{2}$ .

$- 2 x^{2} \sqrt{3 (x^{2} x) y^{2} z^{5}}$

Factor out $z^{4}$ .

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

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

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

Move $x$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$- 2 (x^{1} x^{2}) (y z^{2} \sqrt{3 x z})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 x^{1 + 2} (y z^{2} \sqrt{3 x z})$

Add $1$ and $2$ .

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

Reorder factors in $- 2 x^{3} (y z^{2} \sqrt{3 x z})$ .

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