Algebra II : Number Theory
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #21 : Real Numbers
Which of the following are NOT real numbers?
Real numbers may include positive and negative integers, rational numbers, and also irrational numbers.
Rational numbers are terms that can be expressed as ratios of numbers, such as 
Real numbers cannot include infinity or imaginary numbers, such as 
However, the imaginary term provided in the answer choice is not fully simplified.
This value is a real number.
The term 
The term 
The correct answer is:
Example Question #1 : Types Of Numbers
Which of the following describes the number 
real, natural
imaginary, irrational
real, irrational
real, rational
real, irrational
Example Question #2 : Types Of Numbers
Which of the following sets of numbers contain only natural numbers.
Natural numbers are simply whole, non-negative numbers.
Using this definition, we see only one set of numbers within our answer choices containing only whole, non-negative numbers. Any set containing decimals or negative numbers, will violate our defintion of natural numbers and thus be an incorrect answer.
Example Question #3 : Types Of Numbers
What is the value of 
There is a repeating pattern of four exponent values of 
Example Question #4 : Types Of Numbers
Simplify 
Multiplying out using FOIL (First, Inner, Outer, Last) results in,
Remember that 
Example Question #5 : Types Of Numbers
Which of these numbers is prime?
For a number to be prime it must only have factors of one and itself.
10 has factors 1, 2, 5, 10.
15 has factors 1, 3, 5, 15.
18 has factors 1, 2, 3, 6, 9, 18.
The only factors of 13 are 1 and 13. As such it is prime.
Example Question #6 : Types Of Numbers
Which of the below is an irrational number?
Irrational numbers are defined by the fact that they cannot be written as a fraction which means that the decimals continue forever.
Looking at our possible answer choices we see,
Therefore since,
we can conclude it is irrational.
Example Question #7 : Types Of Numbers
Which of the following describes the type of 
None of these options describe 
An irrational number is a number that cannot be written in fraction form. In other words a nonrepeating decimal is an irrational number.
The 
Therefore, 
Example Question #3 : Types Of Numbers
What is the most specific classification for the x-intercepts to the equation graphed:
real
imaginary
integer
rational
irrational
imaginary
The graph shown never intersects with the x-axis. This means that the x-intercepts must be imaginary.
Example Question #4 : Types Of Numbers
What is the most specific classification for
irrational
natural number
rational
counting number
imaginary
irrational
The square root of 5 is irrational since it is a non-terminating, non-repeating decimal that cannot be expressed as a fraction.
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