1. 7.1 Radical Expressions

2. Objective 1: Find principal square roots of numbers
A square root of a number a is a number c such that
Examples:
25 has a square root of 5 because
25 has a square root of -5 because
-16 does not have a real-number square root because there is no real number c such that

3. Theorem 7-1
-Every positive real number has two real-number square roots. -The number 0 has just one square root, 0 itself. -Negative numbers do not have real-number square roots. Ex. Find the two square roots of 64. The square roots are 8 and -8.

4. Try This
Find the square roots of each number. 9 36
121
-49

5. Definition
The principal square root of a nonnegative number is its nonnegative square root. The symbol represents the principal square root of a. the negative square root of a is written . Ex. Simplify

6. Try This
Simplify

7. Definition
The symbol is a radical sign. An expression written with a radical sign is a radical expression. The expression written under the radical sign is the radicand.

8. Theorem 7-2
For any real number a, . The principal (nonnegative) square root of is the absolute value of a. Ex

9. Try This

10. Objective 2: Find odd and even kth roots
The number c is the cube root of a if
2 is the cube root of 8 because
-5 is the cube root of -125 because
Ex. Simplify.

11. Try This
Simplify

12. Rewrite using exponential notation

13. Try This

14. The number k in is called the index
The number k in is called the index. If k is an odd number, we say that we are finding an odd root. Examples. Find the following

15. Try This
Find the following

16. Theorem 7-3 For any real number a, the following statements are true.
A When k is even.
B. When k is odd.

17. Try This
Find the following