A6kg object has 350j of kinetic energy. find the velocity of the object?

We have no information describing the direction in which
the object is moving, so we're in no position to discuss its
velocity.   ==> We have only speed to work with.

                                      Kinetic energy = (1/2) (mass) (speed²)

                                                   (350 J) = (1/2) (6 kg) (speed²)

Divide each side by  3 kg :    (350J / 3 kg)  =  (speed²)

Take the square root of each side:       Speed  =  10.8 m/s  (rounded)

Units (for the curious/inquisitive):

[Energy] = [work] =        [force] x                [distance]

                             = [mass-distance/time²] x [distance]

                             =  [ kg-meter / sec² ]  x  [ meter ]

                             =  [ kg-meter² / sec² ]  =  Joule

Energy / mass  =  Joule/kg  =  [ meter² / sec² ]  =  (speed²)