Simplify square root of 20* square root of -5

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

Rewrite $- 5$ as $- 1 (5)$ .

$\sqrt{20} \cdot \sqrt{- 1 (5)}$

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$\sqrt{20} \cdot (\sqrt{- 1} \cdot \sqrt{5})$

Rewrite $\sqrt{- 1}$ as $i$ .

$\sqrt{20} \cdot (i \cdot \sqrt{5})$

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

Factor $4$ out of $20$ .

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

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

$\sqrt{2^{2} \cdot 5} \cdot (i \cdot \sqrt{5})$

Pull terms out from under the radical.

$2 \sqrt{5} \cdot (i \cdot \sqrt{5})$

Multiply $2 \sqrt{5} (i \sqrt{5})$ .

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

$2 ({\sqrt{5}}^{1} \sqrt{5}) i$

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

$2 ({\sqrt{5}}^{1} {\sqrt{5}}^{1}) i$

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

$2 {\sqrt{5}}^{1 + 1} i$

Add $1$ and $1$ .

$2 {\sqrt{5}}^{2} i$

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

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

$2 {(5^{\frac{1}{2}})}^{2} i$

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

$2 \cdot 5^{\frac{1}{2} \cdot 2} i$

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

$2 \cdot 5^{\frac{2}{2}} i$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \cdot 5^{\frac{2}{2}} i$

Rewrite the expression.

$2 \cdot 5^{1} i$

Evaluate the exponent.

$2 \cdot 5 i$

Multiply $2$ by $5$ .

$10 i$