Mr. Scott’s
Study Sheet
Test 1
The test will cover everything that was on the first Quiz (fractions, decimals & percents), as well as
everything on this study sheet (sets of numbers, square roots, & properties of numbers).
Sets of Numbers




Natural Numbers (Counting Numbers): 1, 2, 3, 4, 5, 6…
Wh0le Numbers: 0, 1, 2, 3, 4, 5, 6, 7…
Integers: …-4, -3, -2, -1, 0, 1, 2, 3, 4, 5…
Rational Numbers: Any number that can be
𝑎
expressed as a fraction of two integers 𝑏 (where
b≠0). This includes: fractions, repeating decimals,
terminating decimals. REMEMBER: the square root of
a perfect square would be considered rational. For
example: √49 = 7

Irrational Numbers: Any type of number that
cannot be expressed as a fraction of two integers.
This includes: non-repeating, non-terminating
decimals. For example, a number, such as
0.1385875832382485895845992….Notice how it
does not repeat, but it also does not end.
π is an irrational number because it is a never
ending decimal. Any square root of a non-perfect
square is an irrational number.
Square Roots
The square of a number is the product when a number is multiplied by itself.
Examples:
The square of 4 is 42 = 16
The square of 10 is 102 = 100
The square of 14 is 142 = 196
Don’t confuse this with square root!!!
The square root of a number is the number that when multiplied by itself equals a given number.
Examples:
The square root of 225 is √225 = 15
The square root of 196 is √196 = 14
The square root of 81 is √81 =
9
A perfect square is a number that is a square of an integer. Please memorize all of the perfect
squares/square roots up to 225.
√1 = 1
√81 = 9
√25 = 5
√169 = 13
√4 = 2
√100 = 10
√36 = 6
√196 = 14
√9 = 3
√121 = 11
√49 = 7
√225 = 15
√16 = 4
√144 = 12
√64 = 8
How do we approximate a square root?
If we have a non-perfect square root, we can approximate it to the nearest whole number.
Example 1:
√17
The closest perfect square to 17 is 16.
Since √16 = 4, then √17 ≈ 4
Example 2:
√99
The closest perfect square to 99 is 100.
Since √100 = 10, then √99 ≈ 10
How do we evaluate expressions with square roots?
Substitute in your variables.
Solve all of your square roots first.
Example 1:
Let x = 3, y = 6, and z = 9
Solve:
Notice how
√9
9
√𝑥+𝑦
𝑧
=
√3 + 6
9

√9
9
3
1
93
does NOT equal 1. We solved the square root FIRST, then simplified.
Properties of Numbers
Commutative Property of Addition:
Commutative Property of Multiplication:
a+b+c=c+b+a
axbxc=cxbxa
Associative Property of Addition:
Associative Property of Multiplication:
(a + b) + c = a + (b + c)
(a x b) x c = a x (b x c)
Distributive Property:
a (b + c) = ab + ac
a (b – c) = ab – ac
Identity Property of Addition:
Identity Property of Multiplication:
a+0=a
ax1=a
Inverse Property of Addition:
Inverse Property of Multiplication:
a + (-a) = 0
1
ax𝑎=1
Zero Product Property:
ax0=0
Remember! The commutative, associative, identity, and inverse property are for addition and
multiplication only!