Simplify the Radical Expression 5 square root of 50x^3y^3z^3

$5 \sqrt{50 x^{3} y^{3} z^{3}}$

Step 1

Rewrite $50 x^{3} y^{3} z^{3}$ as ${(5 x y z)}^{2} \cdot (2 x y z)$ .

Factor $25$ out of $50$ .

$5 \sqrt{25 (2) x^{3} y^{3} z^{3}}$

Rewrite $25$ as $5^{2}$ .

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

Factor out $x^{2}$ .

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

Factor out $y^{2}$ .

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

Factor out $z^{2}$ .

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

Move $y$ .

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

Move $x$ .

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

Move $2$ .

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

Rewrite $((5^{2} (x^{2})) (y^{2})) z^{2}$ as ${(5 x y z)}^{2}$ .

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

Add parentheses.

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Remove non-negative terms from the absolute value.

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

Step 4

Multiply $5$ by $5$ .

$25 | x y z | \sqrt{2 x y z}$