bell work8/25/14
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Bell Work8/25/14. Evaluate the expression. 10/15/2014. Powers and Exponents. Roots & Irrational Numbers. TSWBAT: evaluate an expression that has an exponent. TSWBAT: find the root of a number. - PowerPoint PPT PresentationTRANSCRIPT
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Bell Work 8/25/14Evaluate the expression.
1. 5 4 2. 7 3 3. 4 6 2
304.
6
455.
596
6.4
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Powers and Exponents
TSWBAT: evaluate an expression that has an exponent.
04/20/23
Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
1.41.5 Roots & Irrational
Numbers
TSWBAT: find the root of a number.
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Warm-UpSimplify the expression.
31. 5
125
5 5 5 4
2. 2
16
2 2 2 2 3
3. 3
27
3 3 3 25 5 4 4 9 3
24. 9
81 9 9
25. 9
81
9 9
27
6.3
49
9
7 7
3 3 81
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Notes• Definitions
- Power= an expression written with a base and an exponent.
Ex.
25- Base
= the number that is used as a factor.
base
- Exponent= tells how many times the base is going to be a factor.
exponent
25
25
Ex.
5 5
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Notes
Now you try.
34
64
Ex.
4 4 4
Simplify each expression.
42
16
Ex.
2 2 2 2 3
2
8
Ex.
2 2 2 16 4 4 4 4 2
35
125
Ex.
5 5 5 3
3
27
Ex.
3 3 3 4
3
81
Ex.
3 3 3 3 25 5 9 3 9 9
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Notes
Now you try.
27
49
Ex.
7 7
Simplify each expression.
27
49
Ex.
7 7
23
4
9
16
Ex.
3 3
4 4
49
26
36
Ex.
6 6
26
36
Ex.
6 6
25
8
25
64
Ex.
5 5
8 8
36
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Notes
Now you try.
3 22 ____ 3Ex.
2 2 2
Compare with <, >, or =.
4 28
3 3
9
2 45 ____ 2 Ex.
5 5 25
2 2 2 2
4 416
3 23 ____ 4Ex.
3 3 3
9 327
4 4
16
223 ____ 3Ex.
3 3
9
3 3 9
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Notes• Definitions
- Square Root= What number times itself equals the radicand.
Ex.
9 3- Perfect Square
= a number whose square root is a whole number.
Ex.0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
- Radicand= The number inside of the square root symbol.
Ex.9 = The radicand is 9.
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Notes
Ex.36 6 Positive Root
Ex.36 6
Ex.36 6
Negative Root
Positive & Negative Root
Ex.36 No Solution No real number times ITSELF
is negative.
1 1
4 2
9 3
16 4
25 5
36 6
49 7
64 8
81 9
100 10
121 11
144 12
Make a table. Find the square root.
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Notes
Ex.
49
Find each root.
7
Ex.
255
Ex.
81No Solution
Ex.
366
Ex.
10010
Ex.
9
Now you try.
No Solution
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Notes
Ex.9
25
Find each root.
3
5
Now you try.
9
25
Ex.49
36
7
649
36
Ex.16
81
4
9
16
81
Ex.1
16
1
41
16
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Notes• Cube Root
= What number times itself 3 times equals the radicand.
3 1 1 3 8 2 3 27 3 3 64 4 3 125 5Make a table. Find the cube root.
Ex.3 27
3
Ex.3 64
4
Ex.3 125
5
Ex.3 8
2
Ex.3 1
1
Ex.3 216
Now you try.
6
3
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Notes
Ex.
38
27
Find each root.
2
3
Now you try.
3
3
8
27
Ex.
3125
64
5
4
3
3
125
64
Ex.
31
64
1
4
3
3
1
64
Ex.
327
125
3
5
3
3
27
125
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Summary
To find the square root of a number just figure out which number times _____ equals the radicand. If it is a fraction, just find the square root of the top and _______ separately. If it is a _____ root do the same thing except find the number that times itself three times equals the _________.
itself
bottom cube
radicand
A power is an expression that has an _________. The base is the factor, and the exponent tells you how many _______there are. To solve a power, just write down the base as many times as the exponent says, then ________.
exponentfactors
multiply
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HomeworkSimplify.
1. 16 2. 81 3. 100
4. 36 5. 49 6. 25
817.
25
18.
25
1009.
49
310. 27 311. 125 312. 125
38
13.27
31
14.64
327
15.125
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Today’s Homework
1. Pencil ONLY.2. Must show all of your work.
• NO WORK = NO CREDIT3. Must attempt EVERY problem.4. Always check your answers.
Rules for Homework
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Today’s Homework
1. Pencil ONLY.2. Must show all of your work.
• NO WORK = NO CREDIT3. Must attempt EVERY problem.4. Always check your answers.
Rules for Homework
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Complete the Ticket Out the Door without talking!!!!!
Talking = time after the bell!
Ticket Out the Door
Put your NAME on the paper.
When finished, turn your paper face DOWN.
Evaluate the expression.
24
Find the root.
36
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Class WorkEvaluate the expression.
31. 2 8 22. 3 9 23. 7 49
34. 5 125 45. 3 81 56. 2 32
27. 3 9 3
8. 3 27 49. 3 81
210. 8 64 511. 3 243 312. 4 64
25
13.3
25
9
24
14.3
16
9
24
15.3
16
9
2 316. 6 ____ 3Compare with <, >, or =.
2 517. 2 ____ 1 2 318. 8 ____ 4