Analytic Geometry Unit 4 Worksheet #5

Analytic Geometry
Unit 4 Worksheet #5
Name____________________________
Simplify the expressions using the properties of radicals and rational exponents
Ex) (
)
Ex) (
(
)
)
(
Ex)
Ex)
√
Ex) √
√
)
√
√
√
√
Ex) [( ) ]
Ex) √(
)
(
)
Ex) (
)
[(
) ]
(
)
(√
)
√
√
√
√
√
Simplify the expressions. Assume all variables are positive
Ex) √
Ex) (
)
To solve equations such as
, we take the cube root of both sides. Alternately,
we can raise both sides of the equation to the power. That is, we raise both sides of
the equations to the power that is the inverse ( or reciprocal) of the power in the
problem. To solve
, we can either square both sides and then take the cube
root, we can take the cube root of both sides and then square them, or we can raise
both sides to the
power.
(
)
(
)
Rewrite each of the following using rational exponents and use inverses to solve
for the variable. (You may need to use a calculator for some of them. Be careful!)
Ex) √
Ex) √
(
)
Ex)
√
( )
(
(
)
)
Complete this assignment on notebook paper
Simplify the expression using the properties of radicals and rational exponents
2) √
1)
5)
4) ( )
7) (
)
√
3)
√
√
6) ( )
√
√
8) √
√
9)
√(
)
(
)
Simplify the expression. Assume all variables are positive
12) √
11) √
10)
√
14)
13)
17) √(
16) √
√
15) (
) (
)
18)
)
√
√
Perform the indicated operation. Assume all variables are positive
19) √
√
(
20)
)
(
)
21) √
√
Rewrite each of the following using rational exponents and use inverses to solve for
the variable
22) √
23)
24) √
√
Review
25) A metalworker wants to make an open
box from a sheet of metal. It will be
formed by cutting equal squares from
each corner as shown. Write the
standard form of the polynomial
expression that represents the volume
of the box.
12 in
x
x
16 in