Cubes & Cube Roots explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
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Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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A cube is the result of multiplying a number by itself three times.
A cube root asks which number was cubed to get the given number.
Cubes and cube roots are useful in volume, measurement, algebra, and number patterns.
The cube of 4 is 4 x 4 x . We write this as .
A perfect cube is a number that can be written as the cube of an integer.
The cube root of 64 is 4 because .
Prime factorisation helps find cube roots because prime factors in a perfect cube can be grouped in threes.
Cube numbers appear naturally when finding the volume of a cube.
Meaning: A cube is a number multiplied by itself three times.
Definition: The cube of a is x a x a.
x 6 x .
Meaning: A perfect cube has an integer cube root.
Definition: A perfect cube is the product of an integer used three times.
125 is a perfect cube because 5 x 5 x .
Meaning: Cube root reverses cubing.
Definition: The cube root of n is a number whose cube is n.
The cube root of 27 is 3 because .
Meaning: This method groups prime factors in threes.
Definition: A cube root can be found by taking one factor from each group of three equal prime factors.
x 2 x 2 x 3 x 3 x 3. Cube roo x .
Meaning: The volume of a cube uses cubing.
Definition: Volume of a cubid.
A cube with side 5 cm has volume c.
Easy
Question: Find .
Medium
Question: Find the cube root of 343.
Exam-level
Question: Find the smallest number by which 48 must be multiplied to make a perfect cube.
Thinking is 15
Why it happens: Cubing is confused with multiplying by 3.
Correct approach: means 5 x 5 x .
Pairing factors for cube roots
Why it happens: Square root method is used by habit.
Correct approach: Cube roots need groups of three equal factors.
Forgetting negative cube roots
Why it happens: Students connect roots only with positive numbers.
Correct approach: A negative number can have a negative cube root, such as cube root o = -2.
What is the difference between square and cube?
A square uses a number two times. A cube uses a number three times.
Why do cube roots use groups of three?
A cube is made by multiplying the same number three times.
Is 1 a perfect cube?
Yes. x 1 x 1.
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