Instead of providing your students with all of the numbers to organize in a real numbers venn diagram, why don't you give them the opportunity to create their own?
This project asks students to label the venn diagram, and give several examples of each set of numbers (i.e. an integer that is also a square root, or a natural number that is also a fraction). Students may then color the diagram.
Two versions of the Venn Diagram have been included. One is completely blank, the other has been modified for students who need accommodations (lines provided for vocabulary and boxes provided for real number examples).
A sample answer key and has been provided. Answers may vary.