To Be Rational or Not To Be Rational - That is the Question!

By Susan LoFranco on Apr 24, 2017

  • Identify a geometric sequence of whole numbers with a whole number common ratio
  • Use repeated multiplication to form a geometric sequence
  • Given an area of a square or volume of a cube, find the length of a side
  • Know that the square root of 2 is irrational
  • Square root, squares, rational and irrational numbers


  • Square Root Worksheet  Square root worksheet
  • Tactile Cubes


In this lesson, after making a tactile representation of squared number student will use a talking calculator to solve for square root and determine if it is a rational or irrational number.

  • Review with the student vocabulary: square, square root, rational, and irrational numbers 
  • With the student, using the tactile cubes placed down on a mat, the number of cubes that would equal 2^2.  The answer should be 4 cubes.  
  • Review with the student that the wording of 2^2 is equal to the square root of 4.  
  • Review with the student that the square root of 4 being equal to 2, a rational number. 
  • Explain that 2 is a rational number and the student can be certain of this because it can be written as a ration 2:1 or fraction 2/1
  • As practice using the talking calculator review with the student how to solve for the square root of 4.  
  • Next, with the student, examine the number 3.  Together using the calculator solve for the square root of 3.  The answer will be 1.732...
  • Ask the student if 1.732... is a rational number.  It is not.  Ask the student to explain how they know it is not a rational number. Answers would be either it can't be a fraction, or written as a ratio.  
  • If the student requires more guided practice the following examples for rational numbers would be the square root of 25, and the square root of 9.  Guided practice for irrational numbers would be the square root of 2 and the square root of 10
  • Provided the student understands the concept, have the student complete the Square Root Worksheet using the media of the students choice. 
  • As an extra activity have the student do an Internet search for some famous Irrational Numbers.  

Rational number collage



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