Simplify the Radical Expression 2 square root of 180x^4yz^3

$2 \sqrt{180 x^{4} y z^{3}}$

Step 1

Rewrite $180 x^{4} y z^{3}$ as ${(6 x^{2} z)}^{2} \cdot (5 y z)$ .

Factor $36$ out of $180$ .

$2 \sqrt{36 (5) x^{4} y z^{3}}$

Rewrite $36$ as $6^{2}$ .

$2 \sqrt{6^{2} \cdot 5 x^{4} y z^{3}}$

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

$2 \sqrt{6^{2} \cdot 5 {(x^{2})}^{2} y z^{3}}$

Factor out $z^{2}$ .

$2 \sqrt{6^{2} \cdot 5 {(x^{2})}^{2} y (z^{2} z)}$

Move $y$ .

$2 \sqrt{6^{2} \cdot 5 {(x^{2})}^{2} z^{2} y z}$

Move $5$ .

$2 \sqrt{6^{2} {(x^{2})}^{2} z^{2} \cdot 5 y z}$

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

$2 \sqrt{{(6 x^{2} z)}^{2} \cdot 5 y z}$

Add parentheses.

$2 \sqrt{{(6 x^{2} z)}^{2} \cdot 5 (y z)}$

Add parentheses.

$2 \sqrt{{(6 x^{2} z)}^{2} \cdot (5 y z)}$

Step 2

Pull terms out from under the radical.

$2 (| 6 x^{2} z | \sqrt{5 y z})$

Step 3

Remove non-negative terms from the absolute value.

$2 (6 x^{2} | z | \sqrt{5 y z})$

Step 4

Multiply $6$ by $2$ .

$12 x^{2} | z | \sqrt{5 y z}$