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Algebraic Expressions and Radical Operations with Examples

Warm up by simplifying various algebraic expressions and learn to add and subtract radical expressions. Practice combining like radicals and simplifying square-root expressions. Apply these concepts to finding perimeters of shapes using radical expressions. Includes quizzes for practice.

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Algebraic Expressions and Radical Operations with Examples

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  1. Warm Up Simplify each expression. 1. 14x + 15y – 12y + x 2. 9xy + 2xy – 8xy 3. –3(a + b) + 15x + 3y 3xy –3a – b + 10

  2. Warm Up Continued Simplify. All variables represent nonnegative numbers. 4. 5. 6.

  3. 11-7 Adding and Subtracting Radical Expressions Holt Algebra 1

  4. Square-root expressions with the same radicand are examples of like radicals.

  5. Like radicals can be combined by adding or subtracting. You can use the Distributive Property to show how this is done: Notice that you can combine like radicals by adding or subtracting the numbers multiplied by the radical and keeping the radical the same.

  6. A. Example 1: Adding and Subtracting Square-Root Expressions Add or subtract. The terms are like radicals. B. The terms are unlike radicals. Do not combine.

  7. the terms are like radicals. Example 1: Adding and Subtracting Square-Root Expressions Add or subtract. C. D. Identify like radicals. Combine like radicals.

  8. Example 2A: Simplify Before Adding or Subtracting Simplify each expression. Simplify. Combine like radicals.

  9. Check It Out! Example 2c Simplify each expression. Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. Combine like radicals.

  10. Example 3: Geometry Application Find the perimeter of the triangle. Give the answer as a radical expression in simplest form. Write an expression for perimeter. Simplify. Combine like radicals.

  11. 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. The perimeter is in. Check It Out! Example 3 Write an expression for perimeter 2 (l + w). Multiply each term by 2 . Simplify. Combine like radicals.

  12. Lesson Quiz: Part I Add or subtract. 1. 2. 3. Simplify each expression. 4. 5.

  13. Lesson Quiz: Part II 6. Find the perimeter of the trapezoid. Give the answer as a radical expression is simplest form.

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