Download Altamont Pre-test - Weatherly Math Maniacs

Exponents, Squares & Square Roots
An exponent is a short way to write repeated multiplication of one factor.
Ex: 2 x 2 x 2 = 23
2 is called the base; 3 is called the exponent.
The exponent tells how many times the base is used as a factor.
Together they can be called a power. We read 23 as “two to the third power.”
Your turn: Write 5 x 5 x 5 x 5 as a power. __________________
A power with exponent two is called a square. 72 can be read “seven squared” or
“seven to the second power.” Why would “square” be the name for power two??
Square Numbers
Here are the first three square numbers: 1, 4, 9, and 16. They are also called
“perfect squares.”
1 = 12
4 = 22
9 = 32
16 = 42
Complete the chart of the perfect squares with the given bases.
Base
1
2
3
4
5
6
7
Square
12 = 1
22 = 4
32 =
42 =
Base
8
9
10
11
12
13
14
Square
Base
15
16
17
18
19
20
25
Square
Since 32 = 9, 3 is called the square root of 9. What is the square root of 225? _____
What is the square root of 169? _____
The notation looks like this:
9  3 . Find
What is the square root of 400? _____
64  ____
121  ____
4  ____
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Practice
1. Find the sum of the squares of the first five non-negative integers.
a) 28b) 30
c) 45
d) 55
2. Evaluate 25 – 24 + 23 - 22
a) 36 b) 20
c) 13
d) 4
3. The sum of two consecutive even numbers is 46. What is the difference between the
squares of these two numbers?
a) 576
b) 484
c) 92
d) 2
4.
Evaluate 22009
-22000
5. Solve for x: 7x3 – 3 = 186
a) 3
b) 4
c) 6
6. Solve for x:
a) 3
d) 9
x 5  4
b) 9
c) 36
d) 81
7. Evaluate 5  8  (7 +9  6)3 . (Do you know PEMDAS?)
8. Evaluate 342 - 232.
9. 4  44 
a) 44
10. 22009 = 22008 + ___
a) 1
b) 45
c) 144
d) 165
b) 2
c) 2008
d) 22008
11. If m and n are positive consecutive even integers,
find m + n if m < 2009 < n.
12. The area of a square is 225 square units.
a) What is the perimeter of the square?
b) If the square has the same perimeter as an equilateral triangle, what is the length of
the base of the equilateral triangle?
13, Evaluate
 410
.
47
a) -64
Challenge:
14. Solve for k: 825 = 45k
a) 10 b) 7.5
c) 5
b) -12
c) 12
d) 64
d) 2.5
15. Evaluate 612  602  412  402
a) 51 b) 50
c) 4 d) 2
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