Step by step
The question
Question: simplify ∛54.
The small 3 says how many times.
∛54 asks: which number, times itself 3 times, makes 54?
1 Find the biggest cube
Cubes are a number times itself 3 times.
2 × 2 × 2 is 8.
3 × 3 × 3 is 27.
We try the biggest first.
Does 27 go into 54?
Yes: 54 divided by 27 is 2.
Careful!
9 is a square, not a cube.
The cube root of 9 is not 3.
We need a number times itself 3 times.
2 Split the root
So 54 is 27 times 2.
We write it under the root.
Rule: a root over a times can be split into two roots.
So it is ∛27 times ∛2.
∛27 is 3, because 3 × 3 × 3 is 27.
We write 3 in place of ∛27.
We leave out the times sign.
2 has no cube in it, so we are done.
So ∛54 = 3∛2.
3 Check
Let's check: we take the answer to the power 3.
∛2 to the power 3 is just 2.
3 × 3 × 3 is 27.
Times 2 is 54.
We get 54 back.
So the answer is right!
Let's look back.
First: find the biggest cube.
Then: split the root.
Last: check.