Simplify square root of 72x^3y^4z^5

$\sqrt{72 x^{3} y^{4} z^{5}}$

Step 1

Rewrite $72 x^{3} y^{4} z^{5}$ as ${(6 x y^{2} z^{2})}^{2} \cdot (2 x z)$ .

Factor $36$ out of $72$ .

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

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

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

Factor out $x^{2}$ .

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

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

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

Factor out $z^{4}$ .

$\sqrt{6^{2} \cdot 2 (x^{2} x) {(y^{2})}^{2} (z^{4} z)}$

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

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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