Question

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

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

Answer 1

Answer:

Step-by-step explanation:

$\sqrt{-16} =\sqrt{-1 \times 16} =\sqrt{(\iota)^2(4)^2} =\pm 4\iota$

Answer 2

Answer:

$\sqrt{-16}=4i$

Step-by-step 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:

$\boxed{\sqrt{-x}=\sqrt{x} \cdot i}$

Therefore, the square root of -16 is:

$\begin{aligned}\sqrt{-16}&=\sqrt{16} \cdot i\\&=\sqrt{4^2} \cdot i\\&=4 \cdot i\\&=4i\end{aligned}$