To extract a .tar.gz file, you use the tar command with the -x (extract), -z (gzip), and -f (file) flags.
$ tar -xzf your_file_name.tar.gz
This will extract all the files into your current directory.
If you want to see a list of the files as they are being extracted, add the -v (verbose) flag. This is highly recommended so you can see the progress.
$ tar -xvzf your_file_name.tar.gz

Assignment
1] Extract the files from 'material_lesson_5.tar.gz'
2] Fix the script 'string_cmp.sh'
3] Convert the 'infinite while loop' in an 'infinite for loop' in the script 'infinite_loop.sh'
4] Explain the ouputs in 'comparison.sh'
5] Modify the script 'prime_num.sh' using let or expr command to perform arithmetic operations
6] Modify the script 'break_ex.sh' to break out of the outer loop
7] Create a 'assignment_lesson_5.tar.gz' file with the assigments.