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Evaluate -2 square root of 15*4 square root of 12

$- 2 \sqrt{15} \cdot 4 \sqrt{12}$

Step 1

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$- 2 \sqrt{15} \cdot (4 \sqrt{4 (3)})$

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

$- 2 \sqrt{15} \cdot (4 \sqrt{2^{2} \cdot 3})$

$- 2 \sqrt{15} \cdot (4 \sqrt{2^{2} \cdot 3})$

Step 2

Pull terms out from under the radical.

$- 2 \sqrt{15} \cdot (4 (2 \sqrt{3}))$

Step 3

Multiply $2$ by $4$ .

$- 2 \sqrt{15} \cdot (8 \sqrt{3})$

Step 4

Multiply $- 2 \sqrt{15} (8 \sqrt{3})$ .

Multiply $8$ by $- 2$ .

$- 16 \sqrt{15} \sqrt{3}$

Combine using the product rule for radicals.

$- 16 \sqrt{3 \cdot 15}$

Multiply $3$ by $15$ .

$- 16 \sqrt{45}$

$- 16 \sqrt{45}$

Step 5

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$- 16 \sqrt{9 (5)}$

Rewrite $9$ as $3^{2}$ .

$- 16 \sqrt{3^{2} \cdot 5}$

$- 16 \sqrt{3^{2} \cdot 5}$

Step 6

Pull terms out from under the radical.

$- 16 (3 \sqrt{5})$

Step 7

Multiply $3$ by $- 16$ .

$- 48 \sqrt{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- 48 \sqrt{5}$

Decimal Form:

$- 107.33126291 \dots$

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