Step by step
The question
Question: simplify ∛250.
The small 3 says how many times.
∛250 asks: which number, times itself 3 times, makes 250?
1 Find the biggest cube
Cubes are a number times itself 3 times.
2 × 2 × 2 is 8.
3 × 3 × 3 is 27.
4 × 4 × 4 is 64.
5 × 5 × 5 is 125.
We try the biggest first.
Does 125 go into 250?
Yes: 250 divided by 125 is 2.
Careful!
25 is a square, not a cube.
The cube root of 25 is not 5.
We need a number times itself 3 times.
2 Split the root
So 250 is 125 times 2.
We write it under the root.
Rule: a root over a times can be split into two roots.
So it is ∛125 times ∛2.
∛125 is 5, because 5 × 5 × 5 is 125.
We write 5 in place of ∛125.
We leave out the times sign.
2 has no cube in it, so we are done.
So ∛250 = 5∛2.
3 Check
Let's check: we take the answer to the power 3.
∛2 to the power 3 is just 2.
5 × 5 × 5 is 125.
Times 2 is 250.
We get 250 back.
So the answer is right!
Let's look back.
First: find the biggest cube.
Then: split the root.
Last: check.