1. Algebra 2 CC 1.4 Evaluate roots of real numbers
Note: = 3 because 32 = 9
= 2 because 23 = 8
= 3 because 34 = 81
= b if bn = a

2. 1. If n is odd, then “a” has one real nth root.
Note: 32 = 9 and (-3)2 = 9 so both 3 and -3 are the square roots of 9. However 2 is the only cube root of 8.
Root Properties of
1. If n is odd, then “a” has one real nth root.
2. If n is even and a>0, then “a” has 2 real nth roots.
3. If n is even and a<0, then “a” has no real roots.
Find the fourth root(s) of 16.
Find the cube root(s) of -8
Find the 5th root(s) of 32

3. indicates the principle nth root
indicates the principle nth root. If there are two roots, the principle root is positive.

4. Rule: a1/n = and am/n = ( )m
Note: (41/2)2 = 4 so 41/2 =
Rule: a1/n = and am/n = ( )m
Evaluate:
361/2
10001/3
82/3
216-2/3
( )3/2

5. Solve
x4 = 16 1/3 x3 + 9 = 0

6. The total mass in kg of a spacecraft that can be propelled by a magnetic sail, is in theory, given by: M = .015m fd4/3 where m is the mass in kg of the magnetic sail, f is the drag force in newtons of the spacecraft, and d is the distance in astronomical units to the sun. Find the total mass of a spacecraft that can be sent to Mars using m=5000kg, f=4.52 N, and d=1.52 AU.

7. assignment
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Problems 14 – 62 even, 65,66,67