1. EQ: How do I simplify and perform operations with radical functions?

2. The side length of a square is the square root of its area. This relationship is shown by a radical symbol. The number or expression under the radical symbol is called the radicand. The radical symbol indicates only the positive square root of a number, called the principal root. To indicate both the positive and negative square roots of a number, use the plus or minus sign (±). or –5 EQ: How do I simplify and perform operations with radical functions?

4. Notice that these properties can be used to combine quantities under the radical symbol or separate them for the purpose of simplifying square-root expressions. A square-root expression is in simplest form when the radicand has no perfect-square factors (except 1) and there are no radicals in the denominator. EQ: How do I simplify and perform operations with radical functions?

5. Find a perfect square factor of 32. Simplify each expression. Example 2: Simplifying Square–Root Expressions Product Property of Square Roots Quotient Property of Square Roots A. B. EQ: How do I simplify and perform operations with radical functions?

6. Product Property of Square Roots Simplify each expression. Example 2: Simplifying Square–Root Expressions Quotient Property of Square Roots C.C. D. EQ: How do I simplify and perform operations with radical functions?

7. Check It Out! Example 2 A. Simplify each expression. B. Find a perfect square factor of 48. Product Property of Square Roots Quotient Property of Square Roots Simplify. EQ: How do I simplify and perform operations with radical functions?

8. Check It Out! Example 2 Simplify each expression. C. D. Product Property of Square Roots Quotient Property of Square Roots EQ: How do I simplify and perform operations with radical functions?

9. If a fraction has a denominator that is a square root, you can simplify it by rationalizing the denominator. To do this, multiply both the numerator and denominator by a number that produces a perfect square under the radical sign in the denominator. EQ: How do I simplify and perform operations with radical functions?

10. Simplify by rationalizing the denominator. Example 3A: Rationalizing the Denominator Multiply by a form of 1. = 2 EQ: How do I simplify and perform operations with radical functions?

11. Simplify the expression. Example 3B: Rationalizing the Denominator Multiply by a form of 1. EQ: How do I simplify and perform operations with radical functions?

12. Check It Out! Example 3a Simplify by rationalizing the denominator. Multiply by a form of 1. EQ: How do I simplify and perform operations with radical functions?

13. Check It Out! Example 3b Simplify by rationalizing the denominator. Multiply by a form of 1. EQ: How do I simplify and perform operations with radical functions?

14. Square roots that have the same radicand are called like radical terms. To add or subtract square roots, first simplify each radical term and then combine like radical terms by adding or subtracting their coefficients. EQ: How do I simplify and perform operations with radical functions?

15. Add. Example 4A: Adding and Subtracting Square Roots EQ: How do I simplify and perform operations with radical functions?

16. Subtract. Example 4B: Adding and Subtracting Square Roots Simplify radical terms. Combine like radical terms. EQ: How do I simplify and perform operations with radical functions?

17. Check It Out! Example 4a Add or subtract. Combine like radical terms. EQ: How do I simplify and perform operations with radical functions?

18. Check It Out! Example 4b Add or subtract. Simplify radical terms. Combine like radical terms. EQ: How do I simplify and perform operations with radical functions?

19. Lesson Quiz: Part I 1. Estimate to the nearest tenth. 6.7 Simplify each expression. 2. 3. 4. 5. EQ: How do I simplify and perform operations with radical functions?

20. Lesson Quiz: Part II Simplify by rationalizing each denominator. 6. 7. 8. 9. Add or subtract. EQ: How do I simplify and perform operations with radical functions?