Question

How do you find the square root of -6 by imaginary numbers

Answer 1

To find the square root of a negative number use the next:

`√(-1)=i`

For -6:

You can write -6 as the product of 6 and -1:

`√(\left(6\right)*\left(-1\right))`

The square root of a product is the same as the product of the square root if each of the factors:

`=√(6)*√(-1)`

As the square root of 6 is not a exact number (it has many decimals) you leave the square root of 6 as it is. The square root of -1 is i; then, the square root of -6 is:

`\begin{gathered} =√(6)*i \\ =√(6)i \end{gathered}`

Then, the square root of -6 is: (√6)i