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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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