Show property of compact operators over Hilbert spaces

Question

A colleague of mine showed me the following problem:

Let H be a Hilbert space, show that every compact operator $T:H\rightarrow H$ is the limit of a succesion of compact operators of finite rank(That is, their range is a finite dimension vectorial space)

Any help would be greatly appreciated :)

Answer 1

Hint: consider the polar decomposition of $T$.