Square Root
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, it is the opposite or inverse operation of squaring a number.
Mathematically, the square root of a number x is written as:
This means you are looking for a number y such that:
y • y = x or y^2 = x
Example:
The square root of 9 is 3, because 3 • 3=9, so sqrt(9) = 3.
The square root of 25 is 5, because 5 • 5=25, so sqrt(25) = 5.
The square root of 16 is 4, because 4 • 4=16, so sqrt(16) = 4.
Important Points:
Every positive number has two square roots: a positive root and a negative root, because both a positive and a negative number squared give the same positive result. For example, sqrt(9) = 3 or -3, because 3^2 = 9 and (-3)^2 = 9.
The square root of 0 is 0, since 0 • 0 = 0.
The square root of a negative number is not a real number, because there is no real number that, when multiplied by itself, gives a negative result. Instead, it is an imaginary number, represented with i, where i^2 = -1.
Thus, the square root is a fundamental mathematical operation used to find values that, when squared, produce the given number.