5.3 Solving Quadratic Equations by Finding Square Roots

What is a Square Root?The opposite of squaring a

number.r is the square root of s if r2 = sPositive numbers have two square

roots: and – is called a radical signThe number inside is the

radicandThe expression is a radical

Properties of Square Roots

Product Property:

Example:

Used to simplify radical expressions.

Simplifying Radical ExpressionsUsing the Product Property:1. Try to find a “perfect square” that is

a factor. 2. Rewrite as a product of two

radicals.3. Take the square root of the perfect

square. Example: Simplify

ExamplesSimplify each radical expression:

Your Turn!Simplify each radical expression.

Properties of Square RootsQuotient Property:

Example:

Simplifying Radical ExpressionsUsing the Quotient Property:1. Rewrite as a quotient of two radicals.We can’t leave a square root on the

bottom!If bottom is a perfect square:

1. Take square roots on top and bottom. 2. Simplify the top if needed.

If bottom is not a perfect square:1. Multiply by the denominator over itself.2. Simplify.◦Called “Rationalizing the Denominator”

Examples:Simplify each radical expression.

Your Turn!Simplify each radical expression.

Solving EquationsSquare roots can be used to solve

some quadratic equations.For example: has two

solutions,

Usually written is read “plus or minus”

To Solve:Get the squared part by itself.Take the square root of both sides.Simplify your answer - NO

DECIMALS!Don’t forget the !

Examples:Solve

Solve

Your Turn!Solve:

Solving Quadratics with ( )Get the squared part by itself.Take the square root of both sides.Then, keep solving to get x alone.

Example: Solve (x – 2)2 = 36

Examples:Solve:3(x + 5)2 = 24

(2x – 1)2 = 49 (x - 7)2 = 80

Your Turn!Solve:(x + 6)2 = 81

Using Quadratic Models

On Earth, when an object is dropped, its height h (in feet), t seconds after being dropped, can be modeled by:

where is the object’s initial height

(note: this model neglects air resistance)

Example:How long will it take an object

dropped from a 550-foot tall tower to land on the roof of a 233-foot tall building?