Download Lesson 15: Powers and Roots

Bell Work:
In the expression 4ac, what is the
constant?
Answer:
4
Lesson 15:
Powers and Roots
Exponent*: Indicates how many
times the base number is to be
used as a factor.
2
In the expression 5 , 5 is the base
and 2 is the exponent.
3
In the expression 5 , we could also
write it as 5 x 5 x 5 = 125.
2
3
We read 5 as “five squared” and 5
as “five cubed.” We say “to the nth
power” if the exponent n is greater
4
than 3. For example, 5 is read as
“five to the fourth power” or just
“five to the fourth.”
Example:
Simplify
5
4
10
4
Answer:
5 x 5 x 5 x 5 = 625
10 x 10 x 10 x 10 = 10,000
Notice that the number of zeros in
10,000 matches the exponent of
10.
Example:
Write the prime factorization of
72 using exponents.
Answer:
72 = 2 x 2 x 2 x 3 x 3
3
72 = 2 x 3
2
We can use exponents with units
of length to indicate units of area.
The formula for the area of a
2
square is A = s . In this formula, A
represents area and s represents
the length of the side.
Example:
The figure shows a square floor
tile that is one foot on each side.
Find the are covered by the tile in
square inches using the area
formula.
12 inches
Answer:
A = 12
2
= 144 inches
2
Exponents can be applied to
variables. If the same variable is a
factor in an expression a number
of times, we can simplify the
expression by writing the variable
with an exponent.
Example:
Express with exponents.
2xxyyyz
Answer:
2x y z
2
3
Radical Expression*: an
expression that indicates the root
of a number.
Radicand*: The number under a
radical sign.
Index*: Indicates a root of a
number.
The inverse of raising a number to
a power is taking a root of a
number. We may use a radical
sign, √ , to indicate a root of a
number.
√25 = 5
3
√125 = 5
If the index is 4 or more, we say
“the nth root.”
√9 = square root of 9
3
√27 = cubed root of 27
4
√125 = the fourth root of 125
Example:
Simplify
√144
3
√27
Answer:
12 x 12 = 144
= 12
3 x 3 x 3 = 27
=3
A number that is a square of a
counting number is a perfect
square. For example, 25 is a
2
perfect square because 5 = 25.
The number 64 is both a perfect
square and a perfect cube.
Is √64 less than or greater than
3
√64?
Answer:
8 x 8 = 64 and 4 x 4 x 4 = 64
3
√64 > √64
Practice:
The floor of a square room is
covered with square foot tiles. If
100 tiles cover the floor, how long
is each side of the room?
Answer:
√100
= 10 feet
Practice:
Name the first three counting
numbers that are perfect squares.
Then find their positive square
roots.
Answer:
(1 x 1) = 1 (2 x 2) = 4 (3 x 3) = 9
√1 = 1
√4 = 2
√9 = 3
HW: Lesson 15 #1-30
Due Next Time