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Algebra1 Adding and Subtracting Radical Expressions

Algebra1 Adding and Subtracting Radical Expressions. Warm Up. Find the domain of each square-root function. 1) y = √(4x – 2) 2) y = -2√(x + 3) 3) y = 1 + √(x + 6). 1) exponential 2) quadratic. Adding and Subtracting Radical Expressions.

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Algebra1 Adding and Subtracting Radical Expressions

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  1. Algebra1Adding and SubtractingRadical Expressions CONFIDENTIAL

  2. Warm Up Find the domain of each square-root function. 1) y = √(4x – 2) 2) y = -2√(x + 3) 3) y = 1 + √(x + 6) 1) exponential 2)quadratic 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: 2√4 + 4√5 = √5(2 + 5) = 7√5 6√x - 2√x = √x(6 - 2) = 4√x Notice that you can combine like radicals by adding or subtracting the numbers multiplied by the radical and keeping the radical the same. CONFIDENTIAL

  4. Adding and Subtracting Square-Root Expressions Add or subtract. • 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) The terms are like radicals. √y = √y. The terms are like radicals. The terms are unlike radicals. Do not combine. Identify like radicals. Combine like radicals. CONFIDENTIAL

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

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

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

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

  13. Now you try! 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. 3) 10√b in. CONFIDENTIAL

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

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

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

  17. Let’s review 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: 2√4 + 4√5 = √5(2 + 5) = 7√5 6√x - 2√x = √x(6 - 2) = 4√x Notice that you can combine like radicals by adding or subtracting the numbers multiplied by the radical and keeping the radical the same. CONFIDENTIAL

  18. Adding and Subtracting Square-Root Expressions Add or subtract. • 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) The terms are like radicals. √y = √y. The terms are like radicals. The terms are unlike radicals. Do not combine. Identify like radicals. Combine like radicals. 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. CONFIDENTIAL

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

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

  23. You did a great job today! CONFIDENTIAL

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