Simplify square root of 5*-4 square root of 20

$\sqrt{5} \cdot - 4 \sqrt{20}$

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

Factor $4$ out of $20$ .

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

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

$\sqrt{5} \cdot (- 4 \sqrt{2^{2} \cdot 5})$

Pull terms out from under the radical.

$\sqrt{5} \cdot (- 4 (2 \sqrt{5}))$

Multiply $2$ by $- 4$ .

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

Multiply $\sqrt{5} (- 8 \sqrt{5})$ .

Raise $\sqrt{5}$ to the power of $1$ .

$- 8 ({\sqrt{5}}^{1} \sqrt{5})$

Raise $\sqrt{5}$ to the power of $1$ .

$- 8 ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 8 {\sqrt{5}}^{1 + 1}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$- 8 {(5^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 8 \cdot 5^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$- 8 \cdot 5^{1}$

Evaluate the exponent.

$- 8 \cdot 5$

Multiply $- 8$ by $5$ .

$- 40$