Do Now 5/4/10 Do Now 5/4/10 Take out HW from last night. Take out HW from last night. Cumulative Test Chapters 1-10 Cumulative Test Chapters 1-10 Copy HW in your planner. Copy HW in your planner. Text p. 723, #4-52 multiples of 4, #67 & Text p. 723, #4-52 multiples of 4, #67 & 68 68 In your notebook, define a perfect In your notebook, define a perfect square in your own words. Then list square in your own words. Then list the squares of the numbers 1 to 20. the squares of the numbers 1 to 20. (remember this?) (remember this?)
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Do Now 5/4/10 Take out HW from last night. Take out HW from last night. Cumulative Test Chapters 1-10 Cumulative Test Chapters 1-10 Copy HW in your planner.
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Do Now 5/4/10Do Now 5/4/10Take out HW from last night.Take out HW from last night.
Cumulative Test Chapters 1-10Cumulative Test Chapters 1-10
Copy HW in your planner.Copy HW in your planner.Text p. 723, #4-52 multiples of 4, #67 & 68Text p. 723, #4-52 multiples of 4, #67 & 68
In your notebook, define a perfect square in In your notebook, define a perfect square in your own words. Then list the squares of the your own words. Then list the squares of the numbers 1 to 20. numbers 1 to 20. (remember this?)(remember this?)
ClassworkClassworkText p. 708, #1-16 all; not 3Text p. 708, #1-16 all; not 3
A radical expression is in A radical expression is in simplest formsimplest form if the following conditions are true: if the following conditions are true:
-No perfect square factors other thanNo perfect square factors other than 1 are in the radicand.1 are in the radicand.
-No fractions are in the radicand.-No fractions are in the radicand.
-No radicals appear in No radicals appear in the the denominator of a denominator of a fraction.fraction.
Product Property of RadicalsProduct Property of Radicals
The square root of a product equals the The square root of a product equals the product of the square roots of the factors. product of the square roots of the factors.
baab
9218 2332
xx 44 xx 22
31648 3434
Try It Out…Try It Out…
32
24
24
216
39x
xx
xx
2
2
9
9
xx 43
234
34
x
xx
xxy 37 2
xxxx 33 When multiplying radicals, multiply the radicands together and multiply When multiplying radicals, multiply the radicands together and multiply the numbers in front of the radical sign together. Then simplify.the numbers in front of the radical sign together. Then simplify.
34
34 2
x
x
22
2
73
73
yx
xxy
73
73 22
xy
yx
Quotient Property of RadicalsQuotient Property of RadicalsThe square root of a quotient equals the The square root of a quotient equals the
quotient of the square roots of the quotient of the square roots of the numerator and denominator. numerator and denominator.
b
a
b
a
5
4
25
16
25
16
9
21
81
21
81
21
Try It Out…Try It Out…
100
13
100
13
100
13
10
13
2
7
x
22
77
xx
x
7
Rationalizing the DenominatorRationalizing the DenominatorWhenever there is a radical (that is not a Whenever there is a radical (that is not a
perfect square) in the denominator, the perfect square) in the denominator, the radical must be eliminated by radical must be eliminated by rationalizing rationalizing the denominator.the denominator.
7
5
7
7
49
75
7
75
Need to Need to rationalize therationalize thedenominatordenominator
Multiply by 1Multiply by 1 Product property Product property of radicalsof radicals
SimplifySimplify
Try It Out…Try It Out…
b3
2
b
b
b 3
3
3
2
b
b
b
b
3
6
9
62
6
7
6
6
6
7
6
67
Need to Need to rationalize therationalize thedenominatordenominator
Multiply by 1Multiply by 1
SimplifySimplify
Adding and Subtract RadicalsAdding and Subtract RadicalsYou can add and subtract radicals that You can add and subtract radicals that
have the same radicands. have the same radicands.
109132104
4835
105132
31635
Think of as combining ‘like terms’Think of as combining ‘like terms’
Look for common radicandsLook for common radicands
SimplifySimplify
3435
39
Try It Out…Try It Out…
253622
3627
2329
22169
2249
237
2236
Multiplying Radical ExpressionsMultiplying Radical Expressions You can multiply radical expressions the same way you You can multiply radical expressions the same way you
multiplied monomials and binomials using the distributive multiplied monomials and binomials using the distributive
property and FOIL.property and FOIL.
54 100
1054
)204(5
49 143 14 43
1421
61427
simplify & combine like termssimplify & combine like terms
)237)(27(
Try It Out…Try It Out…
187 66
66221
66927
)637(6
20 24 25 4
218 simplify & combine like termssimplify & combine like terms
)25)(24(
HomeworkHomework Text p. 723, #4-52 multiples of 4, Text p. 723, #4-52 multiples of 4,