Simplify the Radical Expression -4 square root of 15*(- square root of 3)

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

Step 1

Multiply $- 4 \sqrt{15} (- \sqrt{3})$ .

Multiply $- 1$ by $- 4$ .

$4 \sqrt{15} \sqrt{3}$

Combine using the product rule for radicals.

$4 \sqrt{3 \cdot 15}$

Multiply $3$ by $15$ .

$4 \sqrt{45}$

Step 2

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

Factor $9$ out of $45$ .

$4 \sqrt{9 (5)}$

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

$4 \sqrt{3^{2} \cdot 5}$

Step 3

Pull terms out from under the radical.

$4 (| 3 | \sqrt{5})$

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$4 (3 \sqrt{5})$

Step 5

Multiply $3$ by $4$ .

$12 \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{5}$

Decimal Form:

$26.83281572 \dots$