A square number is the result of squaring a whole number. Integers N1.2 Core Starter A square number is the result of squaring a whole number. Write down some square numbers. What do you notice about the last digit of each number? Investigate some other square numbers to see whether what you saw is still true. Try to explain your result. How can you tell (without using a calculator) that 2 453 765 292 is not a square number? Can you use what you have discovered to tell if a number is a square number? Preamble A relatively straightforward investigation, although some support may be needed for pupils to begin with. Possible content Recognising and using square numbers, pattern spotting, use of a counter-example. Resources None. Solution/Notes Any whole number squared must end in 0, 1, 4, 5, 6 or 9. (This follows from the fact that all integers end in 0, 1, 2, 3, 4, 5, 6 , 7, 8 or 9.) Therefore a number ending in a 2 cannot be a square number. It is not possible to use this method to tell that a number is a square number. It is not true to say that any number ending in 0, 1, 4, 5, 6, or 9 must be a square number (to be true it must ‘work’ all the time; finding just one occasion where it does not ‘work’ means that it is not always true). Examples where it is not true include: 11, 14, 15 etc. Original Material © Cambridge University Press 2009 Original Material © Cambridge University Press 2009