Question

What is the square root of negative 4?

Answer 1

Hint: In this problem, we have to find the square root of the negative number. we should know that the square root of a negative number gives an imaginary unit \[i\]. We can assume that the square root of -1 is denoted by the symbol \[i\], which is a complex number format. We can write the negative term as an imaginary unit and we can take the square root for the given perfect square number.

Complete step by step solution:
Here we have to find the square root of negative 4.
We know that the square root of a negative number gives an imaginary unit \[i\] which is a complex format.
We can now write the negative term as an imaginary unit and we can take the square root for the given perfect square number.
\[\Rightarrow \sqrt{-4}\]
Where, \[\sqrt{-1}=i,\sqrt{4}=2\]
We can now write the square root of negative 4 as
\[\Rightarrow \sqrt{-4}=2i\]

Therefore, the square root of negative 4 is \[2i\].

Note: we should know that, there does not exist any real number which satisfies \[{{x}^{2}}=-4\], in order to find solution for these types of equations, it is extended to a new kind of number system that allows the square root of the negative numbers. We know that the square root of a negative number gives an imaginary unit \[i\] which is a complex format. We can write the negative term as an imaginary unit and we can take the square root for the given perfect square number.