Step by step
The question
Question: simplify ∛16.
The small 3 says how many times.
∛16 asks: which number, times itself 3 times, makes 16?
1 Find the biggest cube
Cubes are a number times itself 3 times.
2 × 2 × 2 is 8.
We try the biggest first.
Does 8 go into 16?
Yes: 16 divided by 8 is 2.
Careful!
16 is a square, not a cube.
The cube root of 16 is not 4.
We need a number times itself 3 times.
2 Split the root
So 16 is 8 times 2.
We write it under the root.
Rule: a root over a times can be split into two roots.
So it is ∛8 times ∛2.
∛8 is 2, because 2 × 2 × 2 is 8.
We write 2 in place of ∛8.
We leave out the times sign.
2 has no cube in it, so we are done.
So ∛16 = 2∛2.
3 Check
Let's check: we take the answer to the power 3.
∛2 to the power 3 is just 2.
2 × 2 × 2 is 8.
Times 2 is 16.
We get 16 back.
So the answer is right!
Let's look back.
First: find the biggest cube.
Then: split the root.
Last: check.