May 2, 2014

Review Quadratics for test re-take †Tuesday†.

Simplifying Radicals Class/Home Work

Today:

TGIF May 2, 2014

2nd Period

Quadratic Formula Test Results

Five Most Missed Questions from

Quadratic Formula Test

What are the roots of

xx 482

1 2

35% correct

Five Most Missed Questions from

Quadratic Formula Test 34% correct

7x2 - x – 13 = -10

7x2 - x – 3 = 0 Use the quadratic formula

−𝒃±√𝒃𝟐−𝟒𝒂𝒄𝟐 𝒂

𝟏±√𝟏+𝟖𝟒𝟏𝟒

33% correct

Solve 3x2 – 13 = 47. Round your solution to the nearest hundredth.

A. + 3.37 B. + 37.89 C. + 13.21 D. + 4.47 E. None

3x2 = 60

x2 = 20

x = + x = + = 2.236

D Solve (3x – 17)2 = 28

31% correct

A. B. D. E. None

3x – 17 = √𝟐𝟖3x = 17 +

√𝟐𝟖(factor out any perfect squares)

3x = 17 + 2 √𝟕

C.

(divide by three)

30% correctFinal Problem:2p2 + 3p – 9 = 0

−𝒃±√𝒃𝟐−𝟒𝒂𝒄𝟐 𝒂

−𝟑±√𝟗+𝟕𝟐𝟒

−𝟑±𝟗𝟒

Quadratic Formula Review

Solve:

This equation is easily solved by factoring:(x – 5)(x – 1)The solutions therefore, are x = 1 and x = 5

−𝒃±√𝒃𝟐−𝟒𝒂𝒄𝟐 𝒂

Quadratic Formula Review

−𝒃±√𝒃𝟐−𝟒𝒂𝒄𝟐 𝒂

𝟖±√𝟐𝟎𝟐

𝟒±√𝟓𝟏

= 6.24 = 1.76

Solve by rounding to the nearest hundredth:

Class Notes Section of Notebook

Square Roots…

Which leads us to…

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.

Simplify each expression.

Product Property of Square Roots

Product Property of Square Roots

A.

Product Property of Square Roots

B.

Simplifying Radicals

Simplify each expression.

Quotient Property of Square Roots

D.

Quotient Property of Square Roots

C.

Solve ‘D’ above with the numerator and denominator as

separate radicals.Simplify numerator first

Simplify each expression.A.

B.

Find a perfect square factor of 48.Product Property of

Square Roots

Quotient Property of Square RootsSimplify.

Simplifying Radicals

Simplify each expression.C.

D.

Product Property of Square Roots

Quotient Property of Square Roots

Simplifying Radicals

Simplifying Radicals w/Variables

x6y7z3 =

Easy

x3y3

z yzx•x •x•x •x •x •y •y •y •y •y •y •y •z •z

•z =

Describe the process in one word:

Practice:

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.

So far, all of our denominators have been monomials. Monday we will rationalize binomial denominators.

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

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

Lesson Quiz: Part I

1. Find to the nearest tenth. 6.7

Simplify each expression.

2. 3. 4.

5. 6. 7.

8.

In the formulas & definitions section of your note book, write the square of each

number from 1-15. †These should be memorized†What you have is a list of perfect

squares from 1 - 225.

Square Roots…