In present time, a weak attention is devoted to real numbers teaching in grammar schools. The students have serious difficulties to determine the representatives of rational and irrational numbers, and to represent a real number on a number axis. This article demonstrates how to make an appropriate use of mathematical software for the visualization of the difference between rational and irrational numbers. We introduce a proposal of visualization of Pythagorean Theorem based on the ancient idea of commensurability. The demonstration of the diference between rational and irrational numbers is also shown on the example of "barcode" and "number walk".