To cube a number means to multiply that number by itself and then multiply the result by the original number once more.
For example, to "cube ", we need to multiply by to make and then multiply this result by once more. We write the "cube of " as so we have
We would then say that "the cube of is ". We could also say " cubed equals ".
The number in the expression is called the power (or exponent).
The act of cubing a number can be represented geometrically. For example, let's start by representing the number with the following collection of two items:
Then we can picture by creating a bigger shape (called a cube) with length, width and height all equal to
There are items in total in our big cube (one little cube is hiding behind the others), indicating that
Clearly, The next few first basic cubes are shown below:
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The cubes of our usual counting numbers are called cube numbers or perfect cubes. We can write them as follows:
What is the value of
To work out we multiply by itself and then multiply the result by once more:
$30^3=$
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a
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$81\,000$ |
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b
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$18\,000$ |
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c
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$3\,000$ |
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d
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$27\,000$ |
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e
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$9\,000$ |
Cubing a negative number always results in another negative number.
This is because a negative times a negative gives a positive value, and then a positive times a negative is a negative again:
For example,
Calculate the value of
To work out we multiply by itself and then multiply the result by again:
$\left(-2\right)^3=$
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a
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$4$ |
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b
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$-4$ |
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c
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$8$ |
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d
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$-6$ |
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e
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$-8$ |
$(-10)^3=$
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a
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$100$ |
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b
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$-1\,000$ |
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c
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$-100$ |
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d
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$1\,000$ |
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e
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$-30$ |
$(-14)^3=$
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a
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$196$ |
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b
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$-196$ |
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c
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$2\,744$ |
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d
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$-2\,744$ |
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e
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$-14$ |
Find the value of cubed.
To work out we multiply by itself and then multiply the result by again:
$\left(\dfrac{1}{3}\right)^3=$
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a
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$\dfrac{1}{9}$ |
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b
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$\dfrac{1}{3}$ |
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c
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$\dfrac{1}{6}$ |
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d
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$\dfrac{1}{27}$ |
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e
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$\dfrac{1}{2}$ |
$\left(\dfrac{2}{3}\right)^3=$
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a
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$\dfrac{8}{9}$ |
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b
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$\dfrac{6}{9}$ |
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c
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$\dfrac{8}{27}$ |
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d
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$\dfrac{4}{27}$ |
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e
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$\dfrac{2}{27}$ |
What is the cube of
To work out we multiply by itself and then multiply the result by once more:
Expressed as a decimal in its simplest form, $(0.4)^3 =$
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a
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b
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c
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d
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e
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$(1.5)^3=$
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a
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$1.5$ |
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b
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$0.375$ |
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c
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$2.25$ |
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d
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$2.75$ |
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e
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$3.375$ |
Expressed as a decimal in its simplest form, $(-1.6)^3=$
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a
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b
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c
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d
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e
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