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, we’ll take a look at 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 into 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 , type
36 + 87
and press
Enter. -
To subtract , type
143 - 46
and press
Enter. -
To multiply , type
13 * 15
and press
Enter. -
To divide , type
132 / 12
and press
Enter.
GeoGebra Instruction 2
Powers and Roots
- 1.
- Open
CASunderViewinMenu. - 2.
- Powers:
To calculate , type
x^pand pressEnter.Roots:
To calculate , type
x^1/nand pressEnter.If want to compute a square root, you can use the command
sqrt(<x>)instead.sqrtis short for “square root”.Note!
GeoGebraonly prints the positive root, even if there’s a negative root too.
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 .
GeoGebra Instruction 3
Algebraic Expressions
Open CAS under
View in
Menu.
-
To compute , type
2a + 3a
and press
Enter. -
To compute , type
a * b * b^2
and press
Enter. You get . If you typeab * b^2
you get , because
GeoGebrainterpretsabas an object, and not the product .
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
CASunderViewiMenu. - 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. PressEnterwhen you’re done.Note!
CASsimplifies fractions automatically.
CAS can also be used for rounding numbers.
GeoGebra Instruction 5
Rounding
- 1.
- Open
CASunderViewiMenu. - 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 decimal places (lower than the number of decimal places there currently are), use
round(<x>, <y>)
where you replace
<x>with your number, and<y>with the number of decimal places.
You can also calculate powers and roots in CAS.
By clicking Expand in the
CAS Toolbar, you can expand parentheses.
GeoGebra Instruction 6
Expanding Parentheses
- 1.
- Open
CASunderViewinMenu. - 2.
- Type your expression in
CASand clickExpandfrom
Toolbar.
CAS can be used to factorize an expression. If it doesn’t change after clicking Factor , it can’t be factorized.
Note! GeoGebra uses the term factor instead of factorize.
GeoGebra Instruction 7
Factorization
- 1.
- Open
CASunderViewinMenu. - 2.
- Type your expression in
CASand clickFactorin
Toolbar.