Recall that raising a number to the power of three is often called "cubing" a number. For example, the expression $$x3 has the following meanings:
$$x3 | a number $$x raised to the power of three | $$x cubed |
Just as the square of a number relates to the area of a square, cubing a number relates to the volume of a cube.
Cubing a number gives the volume of a cube
Let's look at a table of the first ten perfect cubes. A perfect cube is a number that can be expressed as the cube of an integer. For example, the number $$8 is a perfect cube because it can be expressed as $$2×2×2 or $$23.
$$1 | $$= | $$1×1×1 | $$= | $$13 |
$$8 | $$= | $$2×2×2 | $$= | $$23 |
$$27 | $$= | $$3×3×3 | $$= | $$33 |
$$64 | $$= | $$4×4×4 | $$= | $$43 |
$$125 | $$= | $$5×5×5 | $$= | $$53 |
$$216 | $$= | $$6×6×6 | $$= | $$63 |
$$343 | $$= | $$7×7×7 | $$= | $$73 |
$$512 | $$= | $$8×8×8 | $$= | $$83 |
$$729 | $$= | $$9×9×9 | $$= | $$93 |
$$1000 | $$= | $$10×10×10 | $$= | $$103 |
If we are asked to find the cube root of a value, we are being asked, "What number multiplied by itself three times would give this value?"
We might also see the cube root symbol written with a number inside it, for example, $$3√125 represents the cube root of $$125 which is equivalent to $$5 because $$5×5×5=125.
Evaluate $$3√64.
Think: We should read $$3√64 as "the cube root of $$64".
This is the number multiplied by itself three times to make $$64.
We know that $$64=4×4×4.
Do: This means the cube root of $$64 is $$4, so $$3√64=4.
Evaluate $$3√27
Consider $$x3=64.
Complete the rearranged equation:
$$x$$=$$3√
Solve the equation for $$x.