Question

Find the fourth root of \[-4?\]

Answer 1

Hint: Here, we have to find the fourth root of a given number.
But the given number is negative, as we have to find the fourth root is negative, as we have to find the fourth root so we have to find such a number whose four multiplications will be a given negative number.
But if we multiply one number four times we can’t get the negative number, so this A is not possible to find the fourth root of a negative number.

Complete step by step solution:
Given that, there is a number \[-4\] and we have to find its fourth root. As we know that, the fourth root of any positive number will be a real number.
But the fourth root of any negative number can not be a real number.
For example, if we have to find the fourth root of a positive number let suppose it is \[16\] that is \[\sqrt[4]{16}\], So if we want to simplify it we can do it in this way.
As we know that the fourth root means we have to find such a number whose four times multiplication will be the answer of the root number.
That is if we, multiply \[2\] four time we will get \[16\], That is,
\[\begin{align}
  & 2\times 2\times 2\times 2=16 \\
 & \therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{2}^{4}}=16 \\
\end{align}\]
So, far the fourth root of 16, ie. \[\sqrt[4]{16}\] will be \[\sqrt[4]{16}\] \[=\sqrt[4]{{{2}^{4}}}=2\] which is a real number.
But in the given problem, we have to find the fourth root of the negative number \[-4\]. i.e. \[\sqrt[4]{-4}=?\]
As we already wrote, that the four times multiplication of a number must be equal to the under root number.
But if we multiply \[4\] itself if it can't give us the \[4\] itself it can’t give us the \[-4\] number.
Also the given number is an even negative number whose fourth root cannot be possible.
Therefore, the fourth root of \[-4\] can not be found.

Note: In this question, we have to find the fourth root of a negative number.
As we all know, that the fourth root means the multiplication of such a number four times whose answer will be equal to the number under root. But this is only possible for positive numbers.
As we cannot find the fourth root of a negative number because it is not a real number.
As if we multiply any number four times itself it will still not give us the negative answer.
Also, the given number is an even negative number as the fourth root of any even negative number cannot be a real number.
But the cube root of an odd negative number will give us the negative real number.