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

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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

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