What Is a Perfect Square?
Definition
Perfect Square: A number that is a whole number multiplied by itself, such as 1, 4, 9, 16, 25 or 36. The square root of a perfect square is a whole number; for example, √144 = 12.
A perfect square is a whole number multiplied by itself: 1, 4, 9, 16, 25, 36 and so on. The square root of a perfect square is a whole number; for example, √144 = 12. To simplify a square root, you find the largest perfect-square factor of the number and take its root outside the sign.
Where it appears in the formulas
In √x = a × √b, a² is the largest perfect square that divides x. When x is a perfect square, b = 1 and √x = a: √144 = 12. The largest perfect square that divides 180 is 36 = 6², so the square root calculator gives √180 = 6 × √5.