Simplify -4 square root of 8* square root of 10

$- 4 \sqrt{8} \cdot \sqrt{10}$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$- 4 \sqrt{4 (2)} \cdot \sqrt{10}$

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

$- 4 \sqrt{2^{2} \cdot 2} \cdot \sqrt{10}$

$- 4 \sqrt{2^{2} \cdot 2} \cdot \sqrt{10}$

Step 2

Pull terms out from under the radical.

$- 4 (2 \sqrt{2}) \cdot \sqrt{10}$

Step 3

Multiply $2$ by $- 4$ .

$- 8 \sqrt{2} \cdot \sqrt{10}$

Step 4

Multiply $- 8 \sqrt{2} \sqrt{10}$ .

Combine using the product rule for radicals.

$- 8 \sqrt{10 \cdot 2}$

Multiply $10$ by $2$ .

$- 8 \sqrt{20}$

$- 8 \sqrt{20}$

Step 5

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$- 8 \sqrt{4 (5)}$

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

$- 8 \sqrt{2^{2} \cdot 5}$

$- 8 \sqrt{2^{2} \cdot 5}$

Step 6

Pull terms out from under the radical.

$- 8 (2 \sqrt{5})$

Step 7

Multiply $2$ by $- 8$ .

$- 16 \sqrt{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- 16 \sqrt{5}$

Decimal Form:

$- 35.77708763 \dots$

Related Questions