Simplify square root of (576x^4y^3)(32xy^2z)

$\sqrt{(576 x^{4} y^{3}) (32 x y^{2} z)}$

Multiply $32$ by $576$ .

$\sqrt{18432 x^{4} y^{3} (x y^{2} z)}$

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

$\sqrt{18432 (x^{1} x^{4}) y^{3} (y^{2} z)}$

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

$\sqrt{18432 x^{1 + 4} y^{3} (y^{2} z)}$

Add $1$ and $4$ .

$\sqrt{18432 x^{5} y^{3} (y^{2} z)}$

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

$\sqrt{18432 x^{5} y^{2 + 3} z}$

Add $2$ and $3$ .

$\sqrt{18432 x^{5} y^{5} z}$

Rewrite $18432 x^{5} y^{5} z$ as ${(96 x^{2} y^{2})}^{2} \cdot (2 x y z)$ .

Factor $9216$ out of $18432$ .

$\sqrt{9216 (2) x^{5} y^{5} z}$

Rewrite $9216$ as $96^{2}$ .

$\sqrt{96^{2} \cdot 2 x^{5} y^{5} z}$

Factor out $x^{4}$ .

$\sqrt{96^{2} \cdot 2 (x^{4} x) y^{5} z}$

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

$\sqrt{96^{2} \cdot 2 ({(x^{2})}^{2} x) y^{5} z}$

Factor out $y^{4}$ .

$\sqrt{96^{2} \cdot 2 ({(x^{2})}^{2} x) (y^{4} y) z}$

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

$\sqrt{96^{2} \cdot 2 ({(x^{2})}^{2} x) ({(y^{2})}^{2} y) z}$

Move $x$ .

$\sqrt{96^{2} \cdot 2 ({(x^{2})}^{2}) {(y^{2})}^{2} x y z}$

Move $2$ .

$\sqrt{96^{2} ({(x^{2})}^{2}) {(y^{2})}^{2} \cdot 2 x y z}$

Rewrite $(96^{2} ({(x^{2})}^{2})) {(y^{2})}^{2}$ as ${(96 x^{2} y^{2})}^{2}$ .

$\sqrt{{(96 x^{2} y^{2})}^{2} \cdot 2 x y z}$

Add parentheses.

$\sqrt{{(96 x^{2} y^{2})}^{2} \cdot 2 x (y z)}$

Add parentheses.

$\sqrt{{(96 x^{2} y^{2})}^{2} \cdot 2 (x (y z))}$

Add parentheses.

$\sqrt{{(96 x^{2} y^{2})}^{2} \cdot (2 x y z)}$

Pull terms out from under the radical.

$96 x^{2} y^{2} \sqrt{2 x y z}$