Step by step
The question
Question: find ∛−125.
3√−125
The small 3 says how many times.
∛−125 asks: which number, times itself 3 times, makes −125?
? × ? × ? = −125
1 Look at the sign
3 is odd.
A minus number times itself 3 times stays minus.
So the answer is minus.
(−) × (−) × (−) = −
So ∛−125 is minus ∛125.
= −3√125
2 List the cubes
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.
Cubes: 23 = 8, 33 = 27, 43 = 64, 53 = 125
125 is in the list: 5 × 5 × 5 is 125.
5 × 5 × 5 = 125
So ∛−125 = −5.
= −5
3 Check
Let's check: −5 times itself 3 times.
We get −125.
So the answer is right!
(−5) × (−5) × (−5) = −125
Let's look back.
First: look at the sign.
Then: list the cubes.
Last: check.
Answer
= −5