Step by step
The question
Question: solve x³ = 50.
x3 = 50
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.
1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64
x is the cube root of 50.
x = 3√50
50 is not a cube.
It is between 27 and 64.
So the answer is between 3 and 4.
3³ = 27 < 50 < 64 = 4³
A calculator gives 3.684, and so on.
x = 3.684…
To the nearest tenth, x is about 3.7.
x ≈ 3.7
Careful!
A cube has one answer, not two.
A negative number cubed is negative.
Not like x² = 49.
Careful: not x ≈ ±3.7 ✗
2 Check
Let's check: 3.7 times 3.7 times 3.7 is 50.653.
Very close to 50: we rounded.
So the answer is right!
3.7 × 3.7 × 3.7 = 50.653 ≈ 50
Let's look back.
First: cube root of both sides.
Last: check.
Answer
Careful: not x ≈ ±3.7 ✗