Notes Adding, Subtracting, and Multiplying Radical Expressions
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1 Notes 10-2 Adding, Subtracting, and Multiplying Radical Expressions
2 I. Adding and Subtracting Radical Expressions A. Like Radicals Square-root expressions with the same radicand are examples of like radicals.
3 Helpful Hint Combining like radicals is similar to combining like terms. COMPARE: You can combine like radicals by adding or subtracting the numbers multiplied by the radical and keeping the radical the same.
4 B. Basic Examples Example 1: Adding and Subtracting Square-Root Expressions Add or subtract. A. The terms are like radicals. B. The terms are unlike radicals. Do not combine.
5 Add or subtract. C. like radicals. Combine like radicals. the terms are D. Identify like radicals. Combine like radicals.
6 More Examples Add or subtract. a. The terms are like radicals. Combine like radicals. b. The terms are like radicals. Combine like radicals.
7 Add or subtract. c. The terms are like radicals. Combine like radicals. d. Identify like radicals. Combine like radicals.
8 C. Simplifying before combining Sometimes radicals do not appear to be like until they are simplified. Simplify all radicals in an expression before trying to identify like radicals.
9 Example 1: Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. Combine like radicals.
10 Example 2 Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. The terms are unlike radicals. Do not combine.
11 Example 3: Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. Combine like radicals.
12 Example 4 Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. Combine like radicals.
13 Example 5 Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. The terms are unlike radicals. Do not combine.
14 Example 6 Simplify each expression. All variables represent nonnegative numbers. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. Combine like radicals.
15 More examples Ex 7: Ex 8: Ex 9:
16 More Examples Ex 10: x 36x x x x x x x x 6 x x x x 2 3x 5 x x Ex 11: 10 81p 24 p p 83p p 3 2 p p 3 2p p 3
17 D. Applications Example 1: Geometry Application Find the perimeter of the triangle. Give the answer as a radical expression in simplest form. Write an expression for perimeter. Factor 20 using a perfect square. Product Property of Square Roots Simplify. Combine like radicals.
18 II. Multiplying Radical Expressions A. Using the Distributive Property Ex 1: Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Distribute Product Property of Square Roots. Multiply the factors in the second radicand. Factor 24 using a perfect-square factor. Product Property of Square Roots Simplify.
19 Ex 2: Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Distribute Product Property of Square Roots Simplify the radicands. Simplify.
20 Ex 3: Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Distribute Product Property of Square Roots Multiply the factors in the first radicand. Factor 48 using a perfect-square factor. Product Property of Square Roots Simplify.
21 Ex 4: Multiply. Write the product in simplest form. All variables represent nonnegative numbers. Distribute Product Property of Square Roots Factor 50 using a perfect-square factor. Simplify.
22 More Examples Ex 5: Ex 6: 5x x 3 5 x x x 3 25 x x 5 15 x
23 B. Applications Example 1 Find the perimeter of a rectangle whose length is inches and whose width is inches. Give your answer as a radical expression in simplest form. Write an expression for perimeter 2 (l + w). Multiply each term by 2. Simplify. Combine like radicals. The perimeter is in.
24 Lesson Quiz Multiply. Write each product in simplest form. All variables represent nonnegative numbers
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