Step by step
The question
Question: solve y³ = 216.
y3 = 216
y³ means y times y times y.
We want just y.
y³ = y × y × y
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
y is the cube root of 216.
y = 3√216
6 times 6 times 6 is 216.
So y = 6.
y = 6
Careful!
A cube has one answer, not two.
Minus 6, cubed, is minus 216.
Not like x² = 49.
Careful: not y = 6 or y = −6 ✗
2 Check
Let's check: 6 times 6 times 6 is 216.
6 × 6 × 6 = 216
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 y = 6 or y = −6 ✗