Algebra 2 CC 1.4 Evaluate roots of real numbers

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Presentation transcript:

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

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

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

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

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

The total mass in kg of a spacecraft that can be propelled by a magnetic sail, is in theory, given by: M = .015m2 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.

assignment Page 404 Problems 14 – 62 even, 65,66,67