Simplify square root of 4*(- cube root of 125)

$\sqrt{4} \cdot (- \sqrt[3]{125})$

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

$\sqrt{2^{2}} \cdot (- \sqrt[3]{125})$

Pull terms out from under the radical, assuming positive real numbers.

$2 \cdot (- \sqrt[3]{125})$

Rewrite $125$ as $5^{3}$ .

$2 \cdot (- \sqrt[3]{5^{3}})$

Pull terms out from under the radical, assuming real numbers.

$2 \cdot (- 1 \cdot 5)$

Multiply $- 1$ by $5$ .

$2 \cdot - 5$

Multiply $2$ by $- 5$ .

$- 10$