# Algebraic Number/Examples

## Examples of Algebraic Numbers

The algebraic numbers include the following:

### Rational Number is Algebraic

Let $r \in \Q$ be a rational number.

Then $r$ is also an algebraic number.

### $\sqrt 2$ is Algebraic

$\sqrt 2$ is an algebraic number.

### $\sqrt {2 + \sqrt 3}$ is Algebraic

$\sqrt {2 + \sqrt 3}$ is an algebraic number.

### $\sqrt [3] {2 + \sqrt 2}$ is Algebraic

$\sqrt [3] {2 + \sqrt 2}$ is an algebraic number.

### $\sqrt [3] 2 + \sqrt 3$ is Algebraic

$\sqrt [3] 2 + \sqrt 3$ is an algebraic number.

### $\sqrt 3 + \sqrt 2$ is Algebraic

$\sqrt 3 + \sqrt 2$ is an algebraic number.

### $2 - \sqrt 2 i$ is Algebraic

$2 - \sqrt 2 i$ is an algebraic number.

### $\sqrt [3] 4 - 2 i$ is Algebraic

$\sqrt [3] 4 - 2 i$ is an algebraic number.

### Golden Mean is Algebraic

The golden mean $\phi = \dfrac {1 + \sqrt 5} 2$ is an algebraic number.

### Imaginary Unit is Algebraic

The imaginary unit $i$ is an algebraic number.

### $-7$ is Algebraic

$-7$ is an algebraic number.

### $\frac 5 2$ is Algebraic

$\dfrac 5 2$ is an algebraic number.

### $3 - i$ is Algebraic

$3 - i$ is an algebraic number.

### $\sqrt [3] 6$ is Algebraic

$\sqrt [3] 6$ is an algebraic number.

### $\frac 1 3 \paren {1 + i \sqrt 2}$ is Algebraic

$\dfrac 1 3 \paren {1 + i \sqrt 2}$ is an algebraic number.