1 algebra 2: section 7.1 nth roots and rational exponents
TRANSCRIPT
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Algebra 2: Section 7.1
Nth Roots and Rational Exponents
7.1: Evaluating nth Roots• You are familiar with square roots
– 2 is the square root of 4, since 22 = 4.
• This concept can be extended to other types of roots– 2 is the cube root of 8, since 23 = 8– 2 is the fourth root of 16, since 24 = 16– 2 is the fifth root of 32, since 25 = 32– 2 is the nth root of a, since 2n = a
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Rational Exponents1
nna am
nam
na
1 m
na
( )mn a
1m
na
1
( )mn a
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Examples
• Rewrite using rational exponents.
• Rewrite using radical notation.
5
3. 75
27
284. 3
2
831
43
4
35. 7 43 7
31. 271
327
52. a1
5a
4
56. 4 45 4
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Nth Roots Rules for Signs of Answers
• For odd roots (3, 5, 7, etc)
– There is ALWAYS ONLY ONE answer (either + or -)
• For even roots (2, 4, 6, etc)
– If the radical symbol is already in the problem, then use the sign that is in front
– If YOU put the radical symbol in the problem to solve an equation, then there will be two answers (+ and -)
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Examples
• Find the nth root(s) of a7. n = 5, a = -32
8. n = 3: a = 64
9. n = 4: a = 256
10. n = 2: a = 169
What multiplied by itself 5 times equals -32?
What multiplied by itself 3 times equals 64?
4
4
±13
What multiplied by itself 4 times equals 256?
What multiplied by itself 2 times equals 169?
-2
ExamplesSimplify or evaluate each expression:
7
311. 125 5
2412. 16
3613. 0
22 4
30 0
Rational Exponents (examples)
• Simplify or evaluate each expression:
14. 82/3
15. 163/4
16. 4-5/2
3 64 4
34 16 32 8
52
1
4
5
1
2
1
32
23 8
9
Examples
• Solve the equation. Round your answer to two decimal places.
3 8x
2x
317. 5x = 40
Examples
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35 27x
5 3x
2x
318. ( 1) 32y 31 32y
319. 3(x +5) = 81
4.17
3 32 1y
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Homework
P.404
#13-22 all
#24-40 evens
#53-61 all
List of PerfectsPerfect Squares:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Perfect Cubes:
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
Perfect Quads:
1, 16, 81, 256, 625
Perfect Fifths:
1, 32, 243, 1024, 3125