we know for a function to be continuous in Interval then it should be defined at every point in that interval.
we know that inside a root function there can't be a negative number so
t should greater than or equal to 0 and t - 3 should greater than or equal to 0
by taking the intersection of both t should greater than or equal to 3
But at 0 and 3 limit does not exist as the left-hand side limit is not equal to the right-hand side limit.
Therefore, the interval is(1, co) on which the vector-valued function is continuous.