Review for Quadratics re-take Tomorrow

Radical Operations Class/Home Work

Today:May 5, 2014

Quadratic Formula Review

−𝒃±√𝒃𝟐−𝟒𝒂𝒄𝟐 𝒂- 6 = -8x –

6x2

6x2 + 8x – 6 = 0

−𝟖±√𝟔𝟒+𝟏𝟒𝟒𝟏𝟐

−𝟖±√𝟐𝟎𝟖𝟏𝟐

−𝟖±𝟒√𝟏𝟑𝟏𝟐

−𝟐±√𝟏𝟑𝟑

Quadratic Formula Review

−𝟓±√𝟐𝟓+𝟐𝟎𝟎𝟐

w(w + 5) = 50w2 + 5w – 50 = 0 −𝟓±𝟏𝟓

𝟐width = 5; length = 10

4x2 – 4 = 26

304

304

x = +302

Quadratic Formula Review

-1 – 5m2 = - 23

Can there be a solution to this problem?

225

m2 = 225

225

• 55

x = +1105

Class Notes Section of Notebook

Simplifying Radical Expressions by Multiplying

or Dividing

Simplifying RadicalsNotice that these properties can be used to combine quantities under the radical symbol or separate them for the purpose of simplifying square-root expressions.

Separate

Combine

A square-root expression is in simplest form when the radicand has no perfect-square factors (except 1) and there are no radicals in the denominator.

Simplifying Radicals

Simplify the expression.

7 11;3 2

;5 7

5 11 ;x y

Simplifying Radicals w/Variables

32x5y3z2 =

Practice:Review:

25x1727x12x x

83 3x x 6 73 16x x

Bronze Level Silver Level Gold Level

6 7 6 73 16 3 16 x x x x

3 2 2 2 2 x x x x x x x x x x x x x

3 2 2 2 2 x x x x x x x x x x x x x

2 2 3 x x x x x x x 64 3x x

4x2yz xy

If a fraction has a denominator that is a square root, you can simplify it by rationalizing the denominator.

To do this, multiply both the numerator and denominator by a number that produces a perfect square under the radical sign in the denominator. Multiply by a form of 1.

Rationalizing the Denominator

Simplify the expression.

Multiply by a form of 1.

Rationalizing the Denominator

Simplify by rationalizing the denominator.

Multiply by a form of 1.

Rationalizing a Binomial Denominator

Big picture: To remove the radical, we multiply the binomial by another binomial (FOIL) called its conjugate. The conjugate is simply the same binomial with the sign changed between terms.

Multiply the Conjugates

Conjugates

x2 =9

y2 = (2)(2) = 20 9 – 20 = -13

Practice:

8 – 14 = -6

Square roots that have the same radicand are called

like radical terms.

To add or subtract square roots, simplify each radical term and then combine like radical terms by adding or subtracting their coefficients.

Adding & Subtracting Radicals

You can only add or subtract radicals that have the same radicand. The coefficients are combined, the radicand stays the same. (Like the denominator of a fraction)

Example:

= 5 ?Does - = 1? = 4

Add.

Adding & Subtracting Radicals

Can these radicals be added?

= 12 =𝟔+𝟔√𝟔

𝟑𝟑±𝟑√𝟔

𝟑=𝟏±√𝟔

Subtract. Simplify radical terms.

Adding & Subtracting Radicals

Simplify radical terms.

Word ProblemA stadium has a square poster of a football player hung from

the outside wall. The poster has an area of 12,544 ft2. What is

the width of the poster?112 feet wide