1. 11.1 and 11.2 Radicals
List all the perfect squares:

2. Square Roots Symbol: or
Every positive number has both positive and negative square roots.
Principal: just the positive answer
Radical Sign
“Principal” Square Root is the positive 5.

3. Simplify:
Because (9)2 = 81 9 ±8
Not possible
(6)2  -36
(-6)2  -36

4. Rational Numbers
Whole #, fraction, decimal that ends or repeats, square root that is a perfect square

5. Irrational Numbers Square roots that are not perfect squares
Decimal never ends and does not repeat.
Examples of irrational numbers: 

6. Identify the number as irrational or rational

7. Identify the rational number:

8. Real Numbers: All the rational and all the Irrational numbers.

9. Radical Expressions (an expression written under a radical)
Radicand
(the expression written under the radical)
The radicand must be positive!

10. If there is a variable in the radicand:
and solve for the variable to find the values of x that make the expression a real number.

11. Determine the values of x that make the expression a real number.

12. Determine the values of x that make the expression a real number.

13. Perfect Square Radicands Rule: If the radicand contains a variable the square root needs to be in absolute values

14. Explanation

15. Simplify:

16. Simplify:

17. Simplify:

18. Simplify:

19. Homework
worksheet