Do Now:Solve the following equations:

x2 = 25

x2 = 50

Explain your thinking

.

Solving Quadratic Equations by Finding Square Roots

March 5, 2015

Square Root of a Number

If b2 = a, then b is the square root of a.

Example: If 32 = 9, then 3 is the square root of 9.

VocabularyV

All positive real numbers have 2 square roots –

Positive square root – principle square root

Negative square root

Square roots are written with a radical symbol √

Radicand – number inside the radical symbol

Radical

3Radicand

Radical Sign

Positive or Negative

•To indicate that we want both the positive and the negative square root of a radicand we put the symbol ± (read as plus minus) in front of the root.

What about zero?

• Zero has one square root which is 0.

• Negative numbers don't have real square roots since a square is either positive or 0.

• The square roots of negative numbers are imaginary numbers. Example : √-9

A negative outside the Radicand

A negative sign outside the radicand symbolizes the inverse of the square root.

Example: -√9 = -3

Evaluate the expression

1. √64

2. -√64

3. √0

4. ±√0.255. √-4

Which of the following are not perfect squares?

a. -√121

b. -√1.44

c. √0.09

d. √7

√7 is the only irrational number

Radical Expressions

The square root symbol is a grouping symbol.

Evaluate √b2 -4ac when a=1, b=-2, and c=-3

Solving x2 = d

If d > 0, then x2 = d has 2 solution: + and –

If d = 0, then x2 = d has 1 solution: 0

If d < 0, then x2 = d has no real solution.

Solve each equation1. x2 = 2

2. x2 = 5

3. x2 = -1

Rewriting before finding square roots

3x2 – 48 = 0

3x2 = 48

X2 = 16

X = ± √16X = ±4

Falling Objects Model

h = -16t2 + s

h is height in feet

t is time in seconds

s is the initial height the object was dropped

Solve the EquationIf an object is dropped from an initial height 48 feet, how long will it take to reach the ground?

h = -16t2 + s

0 = -16t2 + 48

-48 = -16t2

3 = t2

About 1.7 seconds = t

Properties of Square Rootsp

Product Property –

Example:

Quotient Property -

baab *

b

a

b

a

10210*410*440

2

3

4

3

4

3

Examples

1. √500

2.9

25

Rationalizing the Denominator

You CANNOT leave a radical in the denominator of a fraction!

(the numerator is OK)

Just multiply the top & bottom of the fraction by the radical to “rationalize” the

denominator.

An Example

3

25

3

25

3

5

3*

3*

9

35

3

35

Try these on your own

Solve.

•3 - 5x2 = -9

•3(x-2)2=21