Square RootsObjective

I can simplify radicalsI can use the square root property to solve equations

Square Root Basics

WARM UPSimplify each expressionA)√25B)√x2C)√(x+2)2 D)√(25)(64)E)Describe in your own words what it means

to take the square root of an expression.

Find a perfect square factor of 32.

Simplify each expression. Example 2: Simplifying Square–Root Expressions

Product Property of Square Roots

A.

Quotient Property of Square Roots

B.

OYOSimplify each expression

A.

B.

Find a perfect square factor of 48.

Product Property of Square Roots

Quotient Property of Square Roots

Simplify.

Simplify the following expressionA) √72 – (3)(3)

B) If a = 1 b = 3 and c = 2 find √b2 – 4ac

Read as “plus or minus square root of a.”

Reading Math

Solving Using Square Roots

Why must we include both the plus and the minus?

Solve the equation.

Example 1A: Solving Equations by Using the Square Root Property

Subtract 11 from both sides.

4x2 + 11 = 59

Divide both sides by 4 to isolate the square term.

Take the square root of both sides.

Simplify.

x2 = 12

4x2 = 48

Solve the equation.

Example 1B: Solving Equations by Using the Square Root Property

x2 + 12x + 36 = 28

Factor the perfect square trinomial

Take the square root of both sides.

Subtract 6 from both sides.

Simplify.

(x + 6)2 = 28

Check It Out! Example 1a

4x2 – 20 = 5

Solve the equation.

4x2 = 25Add 20 to both sides.

Divide both sides by 4 to isolate the square term.

Take the square root of both sides.

Simplify.

2 25

4x

Check It Out! Example 1b

x2 + 8x + 16 = 49

Solve the equation.

(x + 4)2 = 49

x = –11, 3

Factor the perfect square trinomial.

Take the square root of both sides.

Subtract 4 from both sides.

Simplify.

x = –4 ± 49

Solve the following for a.

a2 + 2ab + b2 = 25

Challenge Question