1. Warm Up 15x + 3y 3xy –3a – b + 10 Simplify each expression.
1. 14x + 15y – 12y + x
2. 9xy + 2xy – 8xy
3. –3(a + b) +
Simplify. All variables represent nonnegative numbers. 4. 5. 6.
15x + 3y
3xy
–3a – b + 10

2. Adding and Subtracting Radical Expressions

3. Objective Vocabulary Add and subtract radical expressions.
like radicals

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

5. Like radicals can be combined by adding or subtracting
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. Combining like radicals is similar to combining like terms.
Helpful Hint

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

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

9. Try This!
Add or subtract. a.
The terms are like radicals. b.
The terms are like radicals.

10. c. d. The terms are like radicals. Try This! Add or subtract.
Combine like radicals.

11. Sometimes radicals do not appear to be like until they are simplified, Simplify all radicals in an expression before trying to identify like radicals.

12. Simplify Before Adding or Subtracting
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.

13. Simplify Before Adding or Subtracting
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
The terms are unlike radicals. Do not combine.

14. Simplify Before Adding or Subtracting
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.

15. When you write a radicand as a product, make at least one factor a perfect square.
Remember!

16. Try This!
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.

17. Try This!
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
The terms are unlike radicals. Do not combine.

18. Try This!
Simplify each expression.
Factor the radicands using perfect squares.
Product Property of Square Roots.
Simplify.
Combine like radicals.

19. 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.

20. Try This!
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.

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

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