Step by step
The question
Question: solve x³ = 1000.
x3 = 1000
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.
4 times 4 times 4 is 64.
5 times 5 times 5 is 125.
6 times 6 times 6 is 216.
1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216
x is the cube root of 1000.
x = 3√1000
10 times 10 times 10 is 1000.
So x = 10.
x = 10
Careful!
A cube has one answer, not two.
Minus 10, cubed, is minus 1000.
Not like x² = 49.
Careful: not x = 10 or x = −10 ✗
2 Check
Let's check: 10 times 10 times 10 is 1000.
10 × 10 × 10 = 1000
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: not x = 10 or x = −10 ✗