# Algebra II : Types of Numbers

## Example Questions

### Example Question #1 : Types Of Numbers

Which of the following describes the number ?

real, rational

real, natural

real, irrational

imaginary, irrational

real, irrational

Explanation:

is a real number, because you can represent it on the Cartesian coordinate plane, but it is irrational because it cannot be represented by a fraction of two integers. Natural numbers are integers greater than 0.

### Example Question #2 : Types Of Numbers

Which of the following sets of numbers contain only natural numbers.

Explanation:

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  ?

Explanation:

There is a repeating pattern of four exponent values of .

is the same as .

### Example Question #1 : Types Of Numbers

Simplify .

Explanation:

Multiplying out using FOIL (First, Inner, Outer, Last) results in,

.

Remember that

### Example Question #4 : Types Of Numbers

Which of these numbers is prime?

Explanation:

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?

Explanation:

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,

which is an imaginary number but still rational.

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 .

is imaginary, rational

is real, rational

is real, irrational

is imaginary, irrational

is real, irrational

Explanation:

An irrational number is a number that cannot be written in fraction form. In other words a nonrepeating decimal is an irrational number.

The  is an irrational number.

is a real number with a value of .

Therefore, . This is a real but irrational number.

### Example Question #1 : Types Of Numbers

What is the most specific classification for the x-intercepts to the equation graphed:

integer

rational

real

irrational

imaginary

imaginary

Explanation:

The graph shown never intersects with the x-axis. This means that the x-intercepts must be imaginary.

### Example Question #7 : Types Of Numbers

What is the most specific classification for

imaginary

rational

counting number

irrational

natural number

irrational

Explanation:

The square root of 5 is irrational since it is a non-terminating, non-repeating decimal that cannot be expressed as a fraction.

### Example Question #6 : Types Of Numbers

Which of the following is a rational number?