Simplify square root of 10z^5-z^2 square root of 40z

$\sqrt{10 z^{5}} - z^{2} \sqrt{40 z}$

Step 1

Simplify each term.

Rewrite $10 z^{5}$ as ${(z^{2})}^{2} \cdot (10 z)$ .

Factor out $z^{4}$ .

$\sqrt{10 (z^{4} z)} - z^{2} \sqrt{40 z}$

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

$\sqrt{10 ({(z^{2})}^{2} z)} - z^{2} \sqrt{40 z}$

Reorder $10$ and ${(z^{2})}^{2}$ .

$\sqrt{{(z^{2})}^{2} \cdot 10 z} - z^{2} \sqrt{40 z}$

Add parentheses.

$\sqrt{{(z^{2})}^{2} \cdot (10 z)} - z^{2} \sqrt{40 z}$

Pull terms out from under the radical.

$z^{2} \sqrt{10 z} - z^{2} \sqrt{40 z}$

Rewrite $40 z$ as $2^{2} \cdot (10 z)$ .

Factor $4$ out of $40$ .

$z^{2} \sqrt{10 z} - z^{2} \sqrt{4 (10) z}$

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

$z^{2} \sqrt{10 z} - z^{2} \sqrt{2^{2} \cdot 10 z}$

Add parentheses.

$z^{2} \sqrt{10 z} - z^{2} \sqrt{2^{2} \cdot (10 z)}$

Pull terms out from under the radical.

$z^{2} \sqrt{10 z} - z^{2} (2 \sqrt{10 z})$

Multiply $2$ by $- 1$ .

$z^{2} \sqrt{10 z} - 2 z^{2} \sqrt{10 z}$

Step 2

Subtract $2 z^{2} \sqrt{10 z}$ from $z^{2} \sqrt{10 z}$ .

$- z^{2} \sqrt{10 z}$