Simplify square root of -(14a)^2

$\sqrt{- {(14 a)}^{2}}$

Apply the product rule to $14 a$ .

$\sqrt{- 14^{2} a^{2}}$

Raise $14$ to the power of $2$ .

$\sqrt{- 1 \cdot 196 a^{2}}$

Multiply $- 1$ by $196$ .

$\sqrt{- 196 a^{2}}$

Rewrite $- 196 a^{2}$ as ${(14 a)}^{2} \cdot - 1$ .

Factor $196$ out of $- 196$ .

$\sqrt{196 (- 1) a^{2}}$

Rewrite $196$ as $14^{2}$ .

$\sqrt{14^{2} \cdot - 1 a^{2}}$

Move $- 1$ .

$\sqrt{14^{2} a^{2} \cdot - 1}$

Rewrite $14^{2} a^{2}$ as ${(14 a)}^{2}$ .

$\sqrt{{(14 a)}^{2} \cdot - 1}$

Pull terms out from under the radical.

$14 a \sqrt{- 1}$

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

$14 a i$