Perfect Squares

A perfect square is what you get when you square a whole number. Squaring 1 to 12 gives the positive perfect squares up to 144: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144. (0 is one too, since 0 squared is 0.) They are worth knowing by heart, the way you know the times tables, because the next lessons use them all the time.

The name is literal. 16 dots can be laid out as a full 4 by 4 square, with no gaps and no dots left over. 12 dots cannot: a 3 by 3 square uses 9 and leaves 3, and a 4 by 4 square needs 4 more. So 16 is a perfect square and 12 is not.

A quick test rules many numbers out. A perfect square always ends in 0, 1, 4, 5, 6 or 9, because the last digit of a square depends only on the last digit of the number squared. A number ending in 2, 3, 7 or 8 is never a perfect square. The test only rules numbers out, though: 26 ends in 6 and is still not a square.