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Warm-up. Wed. Jan 26. Simplify Completely. No zero or negative exponents 1. 2. Review. Recall: To solve a quadratic equation like the following, use a square root method:. Goal for this lesson: Radical equation such as:. Review: Laws of Exponents. - PowerPoint PPT Presentation
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Warm-up. Wed. Jan 26
Recall:Exponent
PROPERTIESaman = am+n
(am)n = amn
(ab)n = an bn
am/an = am-n
3152 zxx
Simplify Completely. No zero or negative exponents
1.
2.
2
2222
2
3)(
zyx
yzx
Review
124 2 x
124
124
x
x
Recall: To solve a quadratic equation like the following, use a square root method:
Goal for this lesson: Radical equation such as:
327 x
Review: Laws of Exponents
aman amn
am
an am n
(am )n amn
(ab)m ambm
ab
m
am
bm
a m 1
am
Section A.9 nth Roots; Rational Exponents; Radical Equations1. nth Root2. Evaluating nth roots3. Properties of nth roots4. Solving Radical Equations5. Rationalize Denominators
6. Fractional Exponentsa) Simplifying Fractional Exponentsb) Simplifying radicals using rational exponents
7. Simplify radicals some morea) 2 methodsb) More practice
1. nth Roots283
cubed root of 8 is 2 2325 3225
3814 8134
823
ban nba
Definition The principal nth root of a number
is defined as:a
2. Evaluating nth Roots
3251)
6432)
116
43)
3. Properties of nth Roots
ab
n an
bn
abn an bn
amn an m
Product Rule for nth Roots
Quotient Rule for nth Roots
3 a) Practice simplifying radicals
x200 1)
33
85 2) x
35
416 3)y
yx
• Factor the number.• Look for the greatest perfect square
3 b) Multiplying and Combining Radicals
2 6 5 30 1)
5 3 5 2 2)
4. Solving Radical Equations
521 xSolve the following equation.
Isolate radical to one side of equation
Raise both sides to power equal to index of radicand
Check for extraneous solutions
4. Solving Equations with Roots
1 3t3 2 0Solve the following equation.
Isolate radical to one side of equation
Raise both sides to power equal to index of radicand
Check for extraneous solutions
4. Solving Equations with Roots
12 x xSolve the following equation.
Goal: Remove radicals in the denominators
5. Rationalizing Denominators
64
252
Key Idea: For a denominator of the form
Multiply numerator and denominator by:
ba
ba
6. Fractional Exponents
a1
n an
If a is a real number and is an integer, then
n 2
If a is a real number and m and n are integers containing no common factors, with , then,
n 2
mnn mnm
aaa
Ex : 85 3
6 a) Simplifying Fractional ExponentsSimplify the following expressions.
81 5 41)
278
4 32)
6 b) Simplifying Fractional ExponentsSimplify the following expressions.
2/124/143 yxyx
6 c) Practice simplifying radicals using rational exponents
32 1)
3
85 2)
3 58 3)
Examples.Rewrite each radical using rational exponents and simplify.
Day 2: Warm-up
hVr3
Solve the following formula for V:
Solve the following formula for A:
4Ar
2/12344/3 yxyxSimplify:
7. a) Simplify Radicals – 2 methods
Method 1: Look for powers of each term that match the
root.3 458 yx
Method 2:Rewrite using rational exponents and simplify.
3 458 yx
7 a) Simplify Radicals4
3
79
483
xyyx
7 b) Practice Simplifying Radicals
16x 4 y1031) 2) 443 103
7 b) More practice Simplifying Radicals
36x 4 y3 60x 3y 233)
8. Factoring Fractional ExponentsFactor out the GCF.
2/12/3 232323 xxx
8. Factoring Fractional ExponentsFactor out the GCF.
3/52/13/22/12 122121224 xxxxxx
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