1. MTH 065 Elementary Algebra II Chapter 11 Quadratic Functions and Equations Section 11.0 Square Roots (An Introduction to Chapter 11)

2. Solve the Following Equations

4. One more problem … Solve: How do you specify the numbers whose squares are 7? Note: is just a positive number.

5. “Perfect” Squares A number n, where is an integer.

6. Simplifying Square Roots 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)

7. Square Roots of Multiples of Perfect Squares Ask the question: “Is the radicand divisible by a perfect square?”

8. 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: So … That is, in a sense, –1 is a perfect square.

9. Square Roots of Negatives More examples …

10. Simplifying Square Roots The radicand (the number inside the square root symbol) must … not be a perfect square not be negative not have a perfect square factor Also …