Simplify square root of -(x+3)^4

$\sqrt{- {(x + 3)}^{4}}$

Rewrite $- {(x + 3)}^{4}$ as ${({(x + 3)}^{2})}^{2} \cdot - 1$ .

Rewrite ${(x + 3)}^{4}$ as ${({(x + 3)}^{2})}^{2}$ .

$\sqrt{- {({(x + 3)}^{2})}^{2}}$

Reorder $- 1$ and ${({(x + 3)}^{2})}^{2}$ .

$\sqrt{{({(x + 3)}^{2})}^{2} \cdot - 1}$

Pull terms out from under the radical.

${(x + 3)}^{2} \sqrt{- 1}$

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

${(x + 3)}^{2} i$

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$(x + 3) (x + 3) i$

Expand $(x + 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$(x (x + 3) + 3 (x + 3)) i$

Apply the distributive property.

$(x \cdot x + x \cdot 3 + 3 (x + 3)) i$

Apply the distributive property.

$(x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3) i$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$(x^{2} + x \cdot 3 + 3 x + 3 \cdot 3) i$

Move $3$ to the left of $x$ .

$(x^{2} + 3 \cdot x + 3 x + 3 \cdot 3) i$

Multiply $3$ by $3$ .

$(x^{2} + 3 x + 3 x + 9) i$

Add $3 x$ and $3 x$ .

$(x^{2} + 6 x + 9) i$

Apply the distributive property.

$x^{2} i + 6 x i + 9 i$