WPF INotifyPropertyChanged for linked read-only properties

I am trying to understand how to update the UI if I have a read-only property that is dependent on another property, so that changes to one property update both UI elements (in this case a textbox and a read-only textbox. For example:

public class raz : INotifyPropertyChanged
{

  int _foo;
  public int foo
  {
    get
    {
      return _foo;
    }
    set
    {
      _foo = value;
      onPropertyChanged(this, "foo");
    }
  }

  public int bar
  {
    get
    {
      return foo*foo;
    }
  }

  public raz()
  {

  }

  public event PropertyChangedEventHandler PropertyChanged;
  private void onPropertyChanged(object sender, string propertyName)
  {
    if(this.PropertyChanged != null)
    {
      PropertyChanged(sender, new PropertyChangedEventArgs(propertyName));
    }
  }
}

My understanding is that bar will not automatically update the UI when foo is modified. Whats the correct way to do this?