To find the velocity \( v \) of an object that has fallen \( h = 76 \) feet using the formula \( v = \sqrt{64h} \), we first substitute \( h \) into the equation:
\[ v = \sqrt{64 \cdot 76} \]
Next, we calculate \( 64 \cdot 76 \):
\[ 64 \cdot 76 = 4864 \]
Now, we take the square root of 4864:
\[ v = \sqrt{4864} \]
Calculating the square root gives:
\[ v \approx 69.7 \]
Finally, rounding to the nearest hundredth, the velocity \( v \) of an object that has fallen 76 feet is:
\[ \boxed{69.70} \text{ feet per second} \]
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