Definition: A perfect square is a number that equals an integer multiplied by itself, such as 49 = 7 x 7.
What is a perfect square?
It is the result of squaring a whole number. The first twelve are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, and 144.
How do you recognize one?
Its square root is an integer. For 289, test: 17 x 17 = 289, so it is a perfect square. A number ending in 2, 3, 7, or 8 can never be one.
How are they used?
They give clean answers when you use the Pythagorean theorem. A right triangle with legs 9 and 12 has hypotenuse the square root of 81 + 144 = 225, which is 15.
What is the pattern?
Consecutive perfect squares differ by consecutive odd numbers: 4 – 1 = 3, 9 – 4 = 5, 16 – 9 = 7. Between n squared and (n + 1) squared the gap is 2n + 1.
How do you bracket a non-square?
Find the neighbors. The number 70 is between 64 and 81, so its root is between 8 and 9.
What is a common mistake?
Confusing the square of a number with double. The square of 12 is 144, not 24.