The energy stored in a capacitor is given by:
[tex]U= \frac{1}{2}CV^2 [/tex]
where
U is the energy
C is the capacitance
V is the potential difference
The capacitor in this problem has capacitance
[tex]C=3.0 \mu F = 3.0 \cdot 10^{-6} F[/tex]
So if we re-arrange the previous equation, we can calculate the potential V that should be applied to the capacitor to store U=1.0 J of energy on it:
[tex]V= \sqrt{ \frac{2U}{C} }= \sqrt{ \frac{2 \cdot 1.0 J}{3.0 \cdot 10^{-6}F} }=816 V [/tex]
