By definition, an integer is any whole number that is not a fraction.
With this, let's go down the list:
*#sqrt(49)#*
We know that #sqrt(49)# simplified is 7 which is a whole number.
#1.6#
#1.6# is not a whole number to we can rule this out.
#-3/7#
#-3/7# is a fraction so this one is not an integer.
#-55#
#-55# is a whole number and not a fraction so this is an integer.
#36/9#
Once again, we can see #36/9# is a fraction, so it's not an integer.
Final answer:
#sqrt(49)#, #color(red)cancel(1.6)#, #color(red)cancel(-3/7)#, #-55#, #color(red)cancel(36/9)#