Square and Cube Roots

This activity is to visualize irrational vs rational numbers. When introducing students to the idea of irrational numbers, have students draw them out. They can use graph paper and space apart their numbers. For example, if they were drawing the square root of 2 which is 1.414213562373..., they would colour in the 1 square, and then they would count 4 and colour in that square, and then the square 1 away, and then the square 4 away, and then the square 2 away, and so on. Then do this with a repeating decimal as well. The repeating decimal will create a pattern, the irrational number will not. The picture attached is a representation of e. As you can see, there is no pattern and it looks very random. Drawing out a repeating decimal in the same way would make a pattern.