Question

How to find dimension of formula "T=2 pi square root m/k"

Answer 1

write dim of T
write dim of m and k ..... and take sq root of this RHS dimension....
2 pi doesnt count....so remove those
now equate LHS and RHS to check if both dimensions are the same.

Answer 2

The dimension of k is that of a force by a length.
A force is a mass times an acceleration.

Now, all you have to do is work the ratio algebraically, simplify it, and you should end up with a time.