Step by step
The question
Question: solve x³ = −8.
x3 = −8
x³ means x times x times x.
We want just x.
x³ = x × x × x
1 Cube root of both sides
The cube root asks: which number, times itself three times, makes this?
∛27 = ? → ? × ? × ? = 27
The cubes: 1 times 1 times 1 is 1.
2 times 2 times 2 is 8.
3 times 3 times 3 is 27.
1³ = 1, 2³ = 8, 3³ = 27
x is the cube root of −8.
x = 3√−8
A negative number, times itself three times, stays negative: minus times minus is plus, times minus again is minus.
(−2)³ = − × − × − = −
−2 times −2 times −2 is −8.
So x = −2.
x = −2
Careful!
With squares, a negative has no root.
With cubes it does: the answer is negative.
Careful: a negative number has a cube root
2 Check
Let's check: −2 times −2 times −2 is −8.
(−2) × (−2) × (−2) = −8
The same as the right side.
So the answer is right!
Let's look back.
First: cube root of both sides.
Last: check.
Answer
Careful: a negative number has a cube root