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Square Roots

Square Roots. Objective I can simplify radicals I can use the square root property to solve equations. Warm Up. Simplify each expression √25 √x 2 √(x+2) 2 √(25)(64) Describe in your own words what it means to take the square root of an expression. Square Root Basics.

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Square Roots

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  1. Square Roots Objective I can simplify radicals I can use the square root property to solve equations

  2. Warm Up Simplify each expression √25 √x2 √(x+2)2 √(25)(64) Describe in your own words what it means to take the square root of an expression. Square Root Basics

  3. Example 2: Simplifying Square–Root Expressions Simplify each expression. A. Find a perfect square factor of 32. Product Property of Square Roots B. Quotient Property of Square Roots

  4. OYO Simplify each expression A. Find a perfect square factor of 48. Product Property of Square Roots B. Quotient Property of Square Roots Simplify.

  5. Simplify the following expression A) √72 – (3)(3) B) If a = 1 b = 3 and c = 2 find √b2 – 4ac

  6. Reading Math Read as “plus or minus square root of a.” Solving Using Square Roots Why must we include both the plus and the minus?

  7. Example 1A: Solving Equations by Using the Square Root Property Solve the equation. 4x2 + 11 = 59 Subtract 11 from both sides. 4x2 = 48 Divide both sides by 4 to isolate the square term. x2 = 12 Take the square root of both sides. Simplify.

  8. Example 1B: Solving Equations by Using the Square Root Property Solve the equation. x2 + 12x + 36 = 28 Factor the perfect square trinomial (x + 6)2 = 28 Take the square root of both sides. Subtract 6 from both sides. Simplify.

  9. Check It Out! Example 1a Solve the equation. 4x2 – 20 = 5 4x2 = 25 Add 20 to both sides. Divide both sides by 4 to isolate the square term. Take the square root of both sides. Simplify.

  10. x = –4 ± Check It Out! Example 1b Solve the equation. x2 + 8x + 16 = 49 Factor the perfect square trinomial. (x + 4)2 = 49 Take the square root of both sides. Subtract 4 from both sides. x = –11, 3 Simplify.

  11. Challenge Question Solve the following for a. a2 + 2ab + b2 = 25

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