Pre-Algebra Examples

$\sqrt{5 z} (\sqrt{z - 4} \sqrt{5})$

Step 1

Rewrite using the commutative property of multiplication.

$\sqrt{5} \sqrt{5 z} \sqrt{z - 4}$

Step 2

Multiply $\sqrt{5} \sqrt{5 z}$ .

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Step 2.1

Combine using the product rule for radicals.

$\sqrt{5 (5 z)} \sqrt{z - 4}$

Step 2.2

Multiply $5$ by $5$ .

$\sqrt{25 z} \sqrt{z - 4}$

Step 3

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

$\sqrt{5^{2} z} \sqrt{z - 4}$

Step 4

Pull terms out from under the radical.

$5 \sqrt{z} \sqrt{z - 4}$

Step 5

Combine using the product rule for radicals.

$5 \sqrt{(z - 4) z}$

Step 6

Reorder factors in $5 \sqrt{(z - 4) z}$ .

$5 \sqrt{z (z - 4)}$