evaluate nth roots and use rational exponents
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Evaluate nth Roots and Use Rational
ExponentsAlgebra 2
32 = 9
102 = 100
2172 = 47089
Squares and Square Roots
23 = 8
53 = 125
1713 = 5000211
Cubes and Cube Roots
For an integer n greater than 1, if b n = a, then
The nth root of a is equal to b
General Rule
Rational Exponents
Let n be an integer (n > 1), a is a real number and
n is an even integer
a < 0, no real nth roots
a = 0, one real nth root
a > 0, two real nth roots
Real nth Roots of a
Let n be an integer (n > 1), a is a real number and
n is an odd integer
a < 0, one real nth root
a = 0, one real nth root
a > 0, one real nth root
Real nth roots of a
n = 5, a = -32
Answer, n is odd so there is 1 solution:
n = 6, a = 1
Answer – n is even, a is positive so 2 solutions:
Find the real nth root(s) of a
Rational exponents don’t have to be in the form 1/n
Rational Exponents
125 2/3
Answer : 125 2/3 = (125 1/3)2 = 52 = 25
8 -4/3
Answer: 1/16
Evaluate each expression
Solve: 4x5 = 128
Solve: (x – 3)4 = 21
Solve: x6 – 34 = 181
Solving Equations
Solve: 4x5 = 128 x = 2
Solve: (x – 3)4 = 21 x=
Solve: x6 – 34 = 181 x=
Solving Equations
If an expression is irrational then the solution or simplification can be expressed two ways:
Exact answer:
Approximate answer:
Rational Exponent Example
Approximating Roots