Square Roots Objective I can simplify radicals I

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

WARM UP Simplify each expression A) √ 25 B) √x 2 C) √(x+2)2 D)√(25)(64) E)Describe in your own words what it means to take the square root of an expression. Square Root Basics

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

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

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

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

Example 1 A: Solving Equations by Using the Square Root Property Solve the equation. 4 x 2 + 11 = 59 4 x 2 = 48 x 2 = 12 Subtract 11 from both sides. Divide both sides by 4 to isolate the square term. Take the square root of both sides. Simplify.

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

Check It Out! Example 1 a Solve the equation. 4 x 2 – 20 = 5 4 x 2 = 25 Add 20 to both sides. Divide both sides by 4 to isolate the square term. Take the square root of both sides. Simplify.

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

Challenge Question Solve the following for a. a 2 + 2 ab + b 2 = 25