Step by step
The question
Question: find the 4th root of −16.
4√−16
The small 4 says how many times.
The 4th root of −16 asks: which number, times itself 4 times, makes −16?
? × ? × ? × ? = −16
1 Look at the sign
A number times itself 4 times is never negative.
Minus times minus is plus, and the minus signs pair up.
− × − = +
+ × + × + × + = +
But −16 is negative.
So there is no answer: no real number times itself 4 times makes −16.
= no real number
Answer
= no real number