 # How to Use the CAS Calculator in GeoGebra

`CAS` (Computer Algebra System) is the calculator in `GeoGebra`, and has its own view. Open it by clicking `CAS` under `View` in `Menu`.

In this entry, I’ll show you the basics of `CAS`. If you want to learn how to use `CAS` for a specific task in a given subject, like solving systems of equations or differentiation, check out the respective `GeoGebra` entries. The entries are categorized by subject.

By typing your calculation in an empty row in `CAS` and pressing `Enter`, `CAS` will do the calculation for you.

`GeoGebra` Instruction 1

### Arithmetic

Open `CAS` under `View` in `Menu`.

• To add $36+87$, type

36 + 87

and press `Enter`.

• To subtract $143-46$, type

143 - 46

and press `Enter`.

• To multiply $13\cdot 15$, type

13 * 15

and press `Enter`.

• To divide $132:12$, type

132 / 12

and press `Enter`. `GeoGebra` Instruction 2

### PowersandRoots

1.
Open `CAS` under `View` in `Menu`.
2.
Powers:

To calculate ${x}^{p}$, type `x^p` and press `Enter`.

Roots:

To calculate ${x}^{\frac{1}{n}}$, type `x^1/n` and press `Enter`.

If want to compute a square root, you can use the command `sqrt(<x>)` instead. `sqrt` is short for “square root”.

Note! `GeoGebra` only prints the positive root, even if there’s negative root. Algebraic expressions work the same way, but make sure that you use the multiplication symbol (`*`) between the individual symbols. If you for example type `ab`, `GeoGebra` will interpret it as an object with the name “`ab`”, and not $a\cdot b$.

`GeoGebra` Instruction 3

### AlgebraicExpressions

Open `CAS` under `View` in `Menu`.

• To compute $2a+3a$, type

2a + 3a

and press `Enter`.

• To compute $ab\cdot {b}^{2}$, type

a * b * b^2

and press `Enter`. You get $a{b}^{3}$. If you type

ab * b^2

you get $ab\cdot {b}^{2}$, because `GeoGebra` interprets `ab` as an object, and not the product $a\cdot b$. If you want to type a fraction in `CAS`, you need to add a fraction bar (also known as “vinculum”). Here’s how you do it:

`GeoGebra` Instruction 4

### Fractions

1.
Open `CAS` under `View` i `Menu`.
2.
Type `/`. A fraction bar should appear, which consists of two empty fields for the numerator and the denominator, respectively. Type the numerator of your fraction first, and then click on the second field and type your denominator. Press `Enter` when you’re done.

Note! `CAS` simplifies fractions automatically. `CAS` can also be used for rounding numbers.

`GeoGebra` Instruction 5

### Rounding

1.
Open `CAS` under `View` i `Menu`.
2.
If you want to round the number to an integer, use

round(<x>)

where you replace `<x>` with your number.

3.
If you want to round your number to a specific number of decimals (lower than the number of decimals there currently are), use

round(<x>, <y>)

where you replace `<x>` with your number, and `<y>` with the number of decimals. You can also calculate powers and roots in `CAS`.

By clicking `Expand` in the `CAS` `Toolbar`, you can expand parentheses.

`GeoGebra` Instruction 6

### ExpandingParentheses

1.
Open `CAS` under `View` in `Menu`.
2.
Type your expression in `CAS` and click `Expand` from `Toolbar`. `CAS` can be used to factorize an expression. If it doesn’t change after clicking `Factor` , the number can’t be factorized.

Note! `GeoGebra` uses the term factor instead of factorize.

`GeoGebra` Instruction 7

### Factorization

1.
Open `CAS` under `View` in `Menu`.
2.
Type your expression in `CAS` and click `Factor` in `Toolbar`. 