Simplify the Radical Expression -2x square root of 3xy^3z^7

$- 2 x \sqrt{3 x y^{3} z^{7}}$

Step 1

Rewrite $3 x y^{3} z^{7}$ as ${(y z^{3})}^{2} \cdot (3 x y z)$ .

Factor out $y^{2}$ .

$- 2 x \sqrt{3 x (y^{2} y) z^{7}}$

Factor out $z^{6}$ .

$- 2 x \sqrt{3 x (y^{2} y) (z^{6} z)}$

Rewrite $z^{6}$ as ${(z^{3})}^{2}$ .

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

Move $y$ .

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

Move $x$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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