7.1 Radical Expressions.

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Presentation transcript:

7.1 Radical Expressions

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

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.

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

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. 1. 2. 3. 4.

Try This Simplify. 6. 9. 7. 10. 8. 11.

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.

Theorem 7-2 For any real number a, . The principal (nonnegative) square root of is the absolute value of a. Ex. 1. 3. 2. 4.

Try This 12. 13. 14. 15.

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. 1. 2. 3. 4.

Try This Simplify. 16. 17. 18.

Rewrite using exponential notation 1. 2. 3.

Try This 19. 20. 21.

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. 1. 2. 3. 4.

Try This Find the following. 22. 23. 24. 25.

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

Try This Find the following. 26. 29. 27. 30. 28. 31.