Step by step
The question
Question: solve n³ − 10 = 333.
n³ means n times n times n.
We want just n.
1 Remove the − 10
We want n³ by itself.
The − 10 is in the way.
To remove − 10, we add 10.
We do it on both sides, so they stay equal.
− 10 and + 10 make zero.
Cross them out.
Now we have n³ = 343.
2 Cube root of both sides
The cube root asks: which number, times itself three times, makes this?
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.
n is the cube root of 343.
7 times 7 times 7 is 343.
So n = 7.
Careful!
A cube has one answer, not two.
Minus 7, cubed, is minus 343.
Not like x² = 49.
3 Check
Let's check: 7 times 7 times 7 is 343.
Minus 10 is 333.
The same as the right side.
So the answer is right!
Let's look back.
First: remove the − 10.
Then: cube root of both sides.
Last: check.