Review: Simplifying Square Roots of Positive Numbers a.Roots of “perfect” squares –Result is an integer b.Roots of multiples of perfect squares –Result is an integer multiple of a square root (i.e. simplified) c.Roots of all other positive numbers –Result is the square root (i.e. can’t be simplified)
Square Roots of Negatives Since the square of any number is positive, then you might concluded that the square root of a negative number is not “real” … but … Definition: Therefore … That is, in a sense, –1 is a perfect square.
Square Roots of Negatives So … since … for b > 0 …
Imaginary Numbers The set of numbers of the form … –That is, the product of a real number and i.