Step by step
The question
Question: solve x³ = 8/27.
x3 = 827
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 8/27.
x = 3√827
We take the cube root of the top and of the bottom.
2 cubed is 8.
3 cubed is 27.
x = 3√83√27
So x = 2/3.
x = 23
Careful!
A cube has one answer, not two.
Minus 2/3, cubed, is minus 8/27.
Not like x² = 49.
Careful: not x = 23 or x = −23 ✗
2 Check
Let's check: 2/3 times 2/3 times 2/3 is 8/27.
23 × 23 × 23 = 827
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 = 23 or x = −23 ✗