Simplify square root of 72x^3z^3

$\sqrt{72 x^{3} z^{3}}$

Step 1

Rewrite $72 x^{3} z^{3}$ as ${(6 x z)}^{2} \cdot (2 x z)$ .

Factor $36$ out of $72$ .

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

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

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

Factor out $x^{2}$ .

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

Factor out $z^{2}$ .

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$6 x z \sqrt{2 x z}$