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Μάθημα 2: Square roots & cube roots- Square roots of perfect squares
- Worked example: Cube root of a negative number
- Equations with square roots & cube roots
- Dimensions of a cube from its volume
- Square and cube challenge
- Square roots review
- Cube roots review
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Cube roots review
Review cube roots, and try some practice problems.
Cube roots
The cube root of a number is the factor that we multiply by itself three times to get that number.
The symbol for cube root is cube root of, end cube root .
Finding the cube root of a number is the opposite of cubing a number.
Παράδειγμα:
start color #7854ab, 3, end color #7854ab, times, start color #7854ab, 3, end color #7854ab, times, start color #7854ab, 3, end color #7854ab = start color #7854ab, 3, end color #7854ab, start superscript, start color #ff00af, 3, end color #ff00af, end superscript, equals, start color #1fab54, 27, end color #1fab54
So root, start index, start color #ff00af, 3, end color #ff00af, end index = start color #7854ab, 3, end color #7854ab
Want to learn more about finding cube roots? Check out this video.
Finding cube roots
If we can't figure out what factor multiplied by itself three times will result in the given number, we can make a factor tree.
Παράδειγμα:
Here is the factor tree for 64:
Έτσι η παραγοντοποίηση πρώτων αριθμών του 64 είναι 2, times, 2, times, 2, times, 2, times, 2, times, 2.
Ξάχνουμε για την cube root of, 64, end cube root, οπότε θέλουμε να διαιρέσουμε τους πρώτους παράγοντες με τρεις ίδιες ομάδες.
Notice that we can rearrange the factors like so:
Οπότε left parenthesis, 2, times, 2, right parenthesis, cubed, equals, 4, cubed, equals, 64.
Οπότε η cube root of, 64, end cube root είναι 4.
Εξάσκηση
Want to try more problems like this? Check out this exercise:
Finding cube roots
Or this challenge exercise:
Equations with square and cube roots
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