Make Up Tests? Begin Review for Comprehensive Final Exam Simplifying, Adding & Subtracting Radicals Today: TGIF, May 1, 2015
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Make Up Tests?
Begin Review for Comprehensive Final Exam
Simplifying, Adding & Subtracting Radicals
Today:
TGIF, May 1, 2015
Warm-Up/Review:
Find the actual dimensions of the rectangle:
x + 5
x - 1A = 112 (x + 5) (x – 1) = 112
x2 + 4x - 5 = 112
x2 + 4x + 4 = 121(x + 2) 2 = 121
x = 2 + 11 x = -13, x = 9
x2 + 4x = 117
Pencils down, mental math only. What is the resulting trinomial? Square, Double, Square
9m2 – 42mn + 49n2
Solve: 2x2 – 4 = 60
Warm-Up/Review:
At v6math:
Class Notes Section of
Notebook
On a new page, add the heading"Radicals"
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…
Square Roots…
Which leads us to…
Simplifying Radicals
Notice that these properties can be used to combinequantities under the radical symbol or separate them for the purpose of simplifying square-root expressions.
Separate
Combine
Simplify each expression.
Product Property of Square Roots
A.
Product Property of Square RootsB.
Simplifying Radicals
Simplify each expression.
Quotient Property of Square RootsD.
Quotient Property of Square RootsC.
Now, Solve ‘D’ above with the numerator and denominator as separate radicals.
Simplify numerator first Rationalize the denominator
Simplify each expression.
A.
B.
Find a perfect square factor of 48.
Product Property of Square Roots
Quotient Property of Square Roots
Simplify.
Simplifying Radicals
Simplify each expression.
C.
D.
Product Property of Square Roots
Quotient Property of Square Roots
Simplifying Radicals
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.
Simplifying Radicals
Simplify the expression.
Multiply by a form of 1.
Rationalizing the Denominator
Simplify by rationalizing the denominator.
Multiply by a form of 1.
Square roots that have the same radicand are calledlike radical terms.
To add or subtract square roots, first simplify each radical term
and then combine like radical terms by adding or subtracting
their coefficients.
Adding & Subtracting Radicals
Add.
Combine like
radical terms.
Adding & Subtracting Radicals
Subtract.
Simplify radical terms.
Combine like
radical terms.
Simplify radical terms.
Combine like
radical terms.
Adding & Subtracting Radicals
Application
A 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?
x2 = 12,544The formula for area of a square?
112 feet wide
3
Class Work: 4.5Show all work, submit before end of class
1. Simplify
Simplify each expression.
2. 3. 4.
5. 6. 7. 8.
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