\qquad\qquad\quad\large{\pink{ \sf⿻Question⿻}} \\ \\ \qquad\quad{\textsf{Find the square root of -16.}} \\​

Question

`\qquad\qquad\quad\large{\pink{ \sf⿻Question⿻}} \\`


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`\qquad\quad{\textsf{Find the square root of -16.}} \\`​

Answer 1

Explanation:

`√(-16) =√(-1 * 16) =√((\iota)^2(4)^2) =\pm 4\iota`

Answer 2

`√(-16)=4i`

Explanation:

An imaginary number is a non-zero real number multiplied by the imaginary unit,
`i`.

The imaginary unit,
`i`, is defined as the square root of -1.

To find the square root of a negative number, we can express it as:

`\boxed{√(-x)=√(x) \cdot i}`

Therefore, the square root of -16 is:

`\begin{aligned}√(-16)&=√(16) \cdot i\\&=√(4^2) \cdot i\\&=4 \cdot i\\&=4i\end{aligned}`