Simplify the Radical Expression square root of 80x^3yz^5

$\sqrt{80 x^{3} y z^{5}}$

Step 1

Rewrite $80 x^{3} y z^{5}$ as ${(4 x z^{2})}^{2} \cdot (5 x y z)$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5) x^{3} y z^{5}}$

Rewrite $16$ as $4^{2}$ .

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

Factor out $x^{2}$ .

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

Factor out $z^{4}$ .

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

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

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

Move $y$ .

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

Move $x$ .

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

Move $5$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$| 4 x z^{2} | \sqrt{5 x y z}$

Step 3

Remove non-negative terms from the absolute value.

$4 z^{2} | x | \sqrt{5 x y z}$