Simplify -2 square root of 2p*(2 square root of 22)

$- 2 \sqrt{2 p} \cdot (2 \sqrt{22})$

Step 1

Multiply $- 2 \sqrt{2 p} (2 \sqrt{22})$ .

Multiply $2$ by $- 2$ .

$- 4 \sqrt{2 p} \sqrt{22}$

Combine using the product rule for radicals.

$- 4 \sqrt{22 (2 p)}$

Multiply $22$ by $2$ .

$- 4 \sqrt{44 p}$

$- 4 \sqrt{44 p}$

Step 2

Rewrite $44 p$ as $2^{2} \cdot (11 p)$ .

Factor $4$ out of $44$ .

$- 4 \sqrt{4 (11) p}$

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

$- 4 \sqrt{2^{2} \cdot 11 p}$

Add parentheses.

$- 4 \sqrt{2^{2} \cdot (11 p)}$

$- 4 \sqrt{2^{2} \cdot (11 p)}$

Step 3

Pull terms out from under the radical.

$- 4 (2 \sqrt{11 p})$

Step 4

Multiply $2$ by $- 4$ .

$- 8 \sqrt{11 p}$

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