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7.1 nth Roots and Rational exponents
OBJ: evaluate nth roots of real #s using radical notation & rational exponent notation
DO NOW: Evaluate the expression.
1) √9 = 3
2) -√121 = -11
Solve each equation.
4) x2 = 49
x = ±7
5) (x – 1)2 = 64
x–1=±8
x=1±8
x = 9 or x = -7
3) (√25)2 = 25
Finding nth roots
b is an nth root of a IF bn = a
an nth root of a is written
radical
where n is the index of the
Ex 1: Find the indicated real nth root(s) of a
a) n = 2, a = 49
b) n = 4, a = 16
since n is 2, this
means: what #
squared is 49?
±7
d) n = 5, a = 32
since n is 5, this
means: what # to the
5th power is 32?
2
since n is 4, this
means: what # to the
4th power is 16?
±2
e) n = 6, a = 0
since n is 6, this
means: what # to the
6th power is 0?
0
c) n = 3, a = -125
since n is 3, this
means: what #
cubed is -125?
-5
f) n = 2, a = -25
since n is 2, this
means: what #
squared is -25?
no REAL nth roots
Evaluating expressions with rational exponents
am/n = (a1/n)m = (
Rational Exponent
notation
)m
Radical notation
Ex 2:
a)
163/4
=
(161/4)3
= 23
=8
OR
=
 16 
4
= 23
=8
3
b)
27-4/3
 1 
=  3 
 27 
=
1
 
3
=
1
81
HW:
4
4
Using your calculator
Radical notation: n , MATH, a , enter
Rational exponent notation: ( a )
Ex 3:
a) (2197)2/3 =169
b)
( m / n ) enter

7
 280

3
= -11.19
Day 2 practice:
continued…
OBJ: solve equations using nth roots
DO NOW: Solve.
1) 4x2 = 36
x2 = 9
x = ±3
2) (m - 5)2 = 49
m – 5 = ±7
m=5± 7
m = 12 m = -2
Solving Equations Using nth Roots
Ex 4:
a) 2x4 = 162
b) (m - 2)3 = 10
c) x3 = 125
d) (x+4)2 = 0
e) 3x5 = -3
f) x4 – 7 = 9993
Ex 5: from p.403 “Olympias”
The Olympias is a reconstruction of a type of Greek galley
ship used over 2000 years ago. The power P (in kilowatts)
needed to propel the ship at a desired speed s (in knots) can
be modeled by P = 0.0289s3
A crew was able to generate a maximum power of about
10.5kw. What was their speed?
P = 0.0289s3
10.5 = 0.0289s3
363 = s3
s = 7knots
HW: