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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 GeoGebra icon View in GeoGebra icon 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 GeoGebra icon View in GeoGebra icon Menu.

  • To add 36 + 87, type

    36 + 87

    and press Enter.

  • To subtract 143 46, type

    143 - 46

    and press Enter.

  • To multiply 13 15, type

    13 * 15

    and press Enter.

  • To divide 132 : 12, type

    132 / 12

    and press Enter.

Screenshot of GeoGebra showing basic arithmetic in CAS

GeoGebra Instruction 2

Powers and Roots

1.
Open CAS under GeoGebra icon View in GeoGebra icon Menu.
2.
Powers:

To calculate xp, type x^p and press Enter.

Roots:

To calculate x1 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.

Screenshot of GeoGebra showing powers and roots in CAS

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 b.

GeoGebra Instruction 3

Algebraic Expressions

Open CAS under GeoGebra icon View in GeoGebra icon Menu.

  • To compute 2a + 3a, type

    2a + 3a

    and press Enter.

  • To compute ab b2, type

    a * b * b^2

    and press Enter. You get ab3. If you type

    ab * b^2

    you get ab b2, because GeoGebra interprets ab as an object, and not the product a b.

Screenshot of GeoGebra showing basic algebraic calculations in CAS

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 GeoGebra icon View i GeoGebra icon 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.

Screenshot of GeoGebra showing a simplified fraction in CAS

CAS can also be used for rounding numbers.

GeoGebra Instruction 5

Rounding

1.
Open CAS under GeoGebra icon View i GeoGebra icon 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.

Screenshot of GeoGebra showing rounded numbers in CAS

You can also calculate powers and roots in CAS.

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

GeoGebra Instruction 6

Expanding Parentheses

1.
Open CAS under GeoGebra icon View in GeoGebra icon Menu.
2.
Type your expression in CAS and click Expand GeoGebra icon from Toolbar.

Screenshot of GeoGebra showing expanded parentheses in CAS

CAS can be used to factorize an expression. If it doesn’t change after clicking Factor GeoGebra icon, the number can’t be factorized.

Note! GeoGebra uses the term factor instead of factorize.

GeoGebra Instruction 7

Factorization

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

Screenshot of GeoGebra showing factorization in CAS

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