Step by step
The question
Question: solve x³ = 20.
x3 = 20
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 20.
x = 3√20
20 is not a cube.
It is between 8 and 27.
So the answer is between 2 and 3.
2³ = 8 < 20 < 27 = 3³
A calculator gives 2.714, and so on.
x = 2.714…
To the nearest tenth, x is about 2.7.
x ≈ 2.7
Careful!
A cube has one answer, not two.
A negative number cubed is negative.
Not like x² = 49.
Careful: not x ≈ ±2.7 ✗
2 Check
Let's check: 2.7 times 2.7 times 2.7 is 19.683.
Very close to 20: we rounded.
So the answer is right!
2.7 × 2.7 × 2.7 = 19.683 ≈ 20
Let's look back.
First: cube root of both sides.
Last: check.
Answer
Careful: not x ≈ ±2.7 ✗