Simplify 4 square root of -49/64

$4 \sqrt{- \frac{49}{64}}$

Rewrite $- \frac{49}{64}$ as ${(\frac{7 i}{8})}^{2}$ .

$4 \sqrt{{(\frac{7 i}{8})}^{2}}$

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

$4 \frac{7 i}{8}$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$4 \frac{7 i}{4 (2)}$

Cancel the common factor.

$4 \frac{7 i}{4 \cdot 2}$

Rewrite the expression.

$\frac{7 i}{2}$