The cube root of a number n (³√n) is that figure which cubed (i.e. multiplied by itself twice) gives n.
Remember ³√ is the cube root symbol.
If n is a cube number (perfect cube) (1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 etc), its cube root is a whole number.
But if n is a non-cube number (2, 3, 4, 5, 6, 7, 9, 10, 11, 12 etc), its cube root is a decimal and less easy to calculate.
Let's consider the cube roots of cube numbers first.
Which figure cubed (times by itself twice) gives 1?
The answer's 1 because
1³ = 1 x 1 x 1 = 1
What figure cubed (multiplied by itself twice) gives 8?
The answer is 2
2³ = 2 x 2 x 2 = 8
Which figure cubed (times by itself twice) gives 27?
The answer is 3
3³ = 3 x 3 x 3 = 27
The workings out are as follows
Notice all these cube roots are whole numbers.
On your calculator, enter 2 followed by the cube root (³√) button
- you may need to press a shift or 2nd function key to access ³√
The result is
You've calculated ³√2 - the cube root of 2.
It's a decimal, as are the cube roots of other non-cube numbers. For example, use your calculator to check the following
After reading carefully through the examples provided in this lesson, you should now be able to work out
cube roots regardless of whether they're whole numbers or decimals -
albeit sometimes using your calculator!
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