Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor out $z^{4}$ .

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.1.4

Add parentheses.

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

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

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Step 1.3.1

Factor $4$ out of $40$ .

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

Step 1.3.2

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

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

Step 1.3.3

Add parentheses.

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

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

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