1. CONFIDENTIAL 1 Algebra1 Adding and Subtracting Radical Expressions

2. CONFIDENTIAL 2 Warm Up 1) exponential 2) quadratic 1) y = √(4x – 2) 2) y = -2√(x + 3) 3) y = 1 + √(x + 6) Find the domain of each square-root function.

3. CONFIDENTIAL 3 Adding and Subtracting Radical Expressions Square-root expressions with the same radicand are examples of like radicals. 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. 2√4 + 4√5 = √5(2 + 5) = 7√5 6√x - 2√x = √x(6 - 2) = 4√x

4. CONFIDENTIAL 4 Adding and Subtracting Square-Root Expressions A)3√7 + 8√7 = √7(3 + 8) = 11√7 B) 9√y - √y = √y(9 - 1) = 8√y C) 12√2 - 4√11 = √x(6 - 2) = 4√x D) -8√(3d) + 6√(2d) + 10√(3d) = √(3d)(10 - 8) + 6√(2d) = 2√(3d) + 6√(2d) Add or subtract. √y = √y. The terms are like radicals. The terms are like radicals. The terms are unlike radicals. Do not combine. Identify like radicals. Combine like radicals.

5. CONFIDENTIAL 5 Now you try! 1a) -√7 1b) 3√3 1c) 8√n 1d) √(2s) + 8√(5s) Add or subtract. 1a) 5√7 - 6√7 1b) 8√3 - 5√3 1c) 4√n + 4√n 1d) √(2s) - √(5s) + 9 √(5s)

6. CONFIDENTIAL 6 Sometimes radicals do not appear to be like until they are simplified. Simplify all radicals in an expression before trying to identify like radicals.

7. CONFIDENTIAL 7 Simplifying Before Adding or Subtracting A)√(12) + √(27) = √{(4)(3)} + √{(9)(3)} = √4√3 + √9√3 = 2√3 + 3√3 = √3(2 + 3) = 5√3 Add or subtract. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. Combine like radicals.

8. CONFIDENTIAL 8 B) 3√8 + √(45) = 3√{(4)(2)} + √{(9)(5)} = 3√4√2 + √9√5 = 3(2)√2 + 3√5 = 6√2 + 3√5 Factor the radicands using perfect squares. Product Property of Square Roots Simplify. The terms are unlike radicals. Do not combine.

9. CONFIDENTIAL 9 C) 5√(28x) - 8√(7x) = 5√{(4)(7x)} - 8√(7x) = 5√4√(7x) - 8√(7x) = 5(2)√(7x) - 8 √(7x) = 10√(7x) - 8 √(7x) = 2√(7x) Factor 28x using a perfect square. Product Property of Square Roots Simplify. Combine like radicals.

10. CONFIDENTIAL 10 D) √(125b) + 3√(20b) - √(45b) = √{(25)(5b)} + 3√{(4)(5b)} - √{(9)(5b)} = √(25)√(5b) + 3√4√(5b) - √9√(5b) = 5√(5b) + 3(2)√(5b) - 3√(5b) = 5√(5b) +6√(5b) - 3√(5b) = 8√(5b) Factor the radicands using perfect squares. Product Property of Square Roots Simplify. Combine like radicals.

11. CONFIDENTIAL 11 Now you try! 2a) 5√6 2b) 9√3 2c) 5√(3y) Add or subtract. 2a) √(54) + √(24) 2b) 4√(27) - √(18) 2c) √(12y) + √(27y)

12. CONFIDENTIAL 12 Geometry Application A)12 + 5√7 + √(28) = 12 + 5√7 + √{(4)(7)} = 12 + 5√7 + √4√7 = 12 + 5√7 + 2√7 = 12 + 7√7 Write an expression for perimeter. Product Property of Square Roots Simplify. Find the perimeter of the triangle. Give your answer as a radical expression in simplest form. Combine like radicals. Factor 28 using a perfect square. The perimeter is (12 + 7√7) cm.

13. CONFIDENTIAL 13 Now you try! 3) 10√b in. 3) Find the perimeter of a rectangle whose length is 2√b inches and whose width is 3√b inches. Give your answer as a radical expression in simplest form.

14. CONFIDENTIAL 14 Assessment 1)14√3 - 6√3 2)9√5 + √5 3)6√2 + 5√2 - 15√2 1) 8√3 2) 10√5 3) -4√2

15. CONFIDENTIAL 15 Simplify each expression. 4) 2√2 5) 17√3 6) 33√3 7) -√(5x) 8) 2√(7c)+18√(6c) 9) 8√(2t)-4√(3t) 4)√(32) - √(8) 5)4√(12) + √(75) 6)2√3 + 5√(12) - 15√(27) 7)√(20x) - √(45x) 8)√(28c) + 9√(24c) 9)√(50t) - 2√(12t) + 3√(2t)

16. CONFIDENTIAL 16 10) Find the perimeter of the trapezoid shown. Give your answer as a radical expression in simplest form. 10) 12√2 in

17. CONFIDENTIAL 17 Adding and Subtracting Radical Expressions Square-root expressions with the same radicand are examples of like radicals. 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. 2√4 + 4√5 = √5(2 + 5) = 7√5 6√x - 2√x = √x(6 - 2) = 4√x Let’s review

18. CONFIDENTIAL 18 Adding and Subtracting Square-Root Expressions A)3√7 + 8√7 = √7(3 + 8) = 11√7 B) 9√y - √y = √y(9 - 1) = 8√y C) 12√2 - 4√11 = √x(6 - 2) = 4√x D) -8√(3d) + 6√(2d) + 10√(3d) = √(3d)(10 - 8) + 6√(2d) = 2√(3d) + 6√(2d) Add or subtract. √y = √y. The terms are like radicals. The terms are like radicals. The terms are unlike radicals. Do not combine. Identify like radicals. Combine like radicals.

19. CONFIDENTIAL 19 Sometimes radicals do not appear to be like until they are simplified. Simplify all radicals in an expression before trying to identify like radicals.

20. CONFIDENTIAL 20 Simplifying Before Adding or Subtracting A)√(12) + √(27) = √{(4)(3)} + √{(9)(3)} = √4√3 + √9√3 = 2√3 + 3√3 = √3(2 + 3) = 5√3 Add or subtract. Factor the radicands using perfect squares. Product Property of Square Roots Simplify. Combine like radicals.

21. CONFIDENTIAL 21 C) 5√(28x) - 8√(7x) = 5√{(4)(7x)} - 8√(7x) = 5√4√(7x) - 8√(7x) = 5(2)√(7x) - 8 √(7x) = 10√(7x) - 8 √(7x) = 2√(7x) Factor 28x using a perfect square. Product Property of Square Roots Simplify. Combine like radicals.

22. CONFIDENTIAL 22 Geometry Application A)12 + 5√7 + √(28) = 12 + 5√7 + √{(4)(7)} = 12 + 5√7 + √4√7 = 12 + 5√7 + 2√7 = 12 + 7√7 Write an expression for perimeter. Product Property of Square Roots Simplify. Find the perimeter of the triangle. Give your answer as a radical expression in simplest form. Combine like radicals. Factor 28 using a perfect square. The perimeter is (12 + 7√7) cm.

23. CONFIDENTIAL 23 You did a great job today!