ALGEBRA 2 /TRIGONOMETRY
Name _______________________
Objective:
a. Evaluate nth roots of real numbers using both radical notation and
rational exponent notation.
b. Use nth roots to solve real-life problems.
Find the square root of 25.
When we use the symbol √
, we are actually evaluating _________________.
n = _______, when we evaluate the square root of a number.
If we have some other root (n) that we want to evaluate, consider the symbol
below.
√
Instead of the radical √ , we can write the same expression as ______________.
Real Nth Roots
 If n is odd, then a has one real nth root: ___________________________.
 If n is even and a > 0, then a has two real nth roots: _____________________.
 If n is even and a = 0, then a has one nth root: _____________________.
 If n is even and a < 0, then a has ________________________________.
Examples
Find the indicated real nth root(s) of a.
1) n = 2, a = 49
2) n = 3, a = -125
3) n = 4, a = 16
Example to Try
Find the indicated real nth root(s) of a.
1) n = 3, a = 27
2) n = 5, a = 3125
3) n = 4, a = -1296
Rational Exponents
So far, we have examined radicals with nth roots that can be rewritten with rational
exponents in the form of
Let
. What if we had to evaluate
be an nth root of a, and let m be a positive integer.
⁄
⁄

⁄
⁄

⁄
√
⁄
√
Example
1)
⁄
a. use radical notation:
b. use rational exponent notation:
2)
⁄
a. use radical notation:
b. use rational exponent notation:
⁄
?
ALGEBRA 2 /TRIGONOMETRY
Name _______________________
Examples to Try
Evaluate the expression.
1)
3)
⁄
2) √
⁄
4) √
Rational Exponents in the Greek World
How fast can a Greek galley ship travel?
The Olympias is a reconstruction of a trireme, a
type of Greek galley ship used over 2000 years
ago. The power P (in kilowatts) needed to
propel the Olympias at a desired speed s (in knots) can be modeled by this
equation:
A volunteer crew (170 rowers) of the Olympias was able to generate a
maximum power of about 10.5 kilowatts. What was their greatest speed?
PRACTICE
Write each expression in radical form.
1)
2)
3)
4)
Write each expression in rational form.
5)
6)
7)
8)
Find the indicated real nth root(s) of a.
9) n = 2, a = 64
10) n = 3, a = -8
11) n = 6, a = -1
12) n = 4, a = 81
Solve the equation
13)
14)
15)
16)