Simplify square root of negative 48

1 answer:

5 0

$\bf \sqrt{-48}\qquad 
\begin{cases}
48=2\cdot 2\cdot 2\cdot 2\cdot 3\\
\qquad 2^2\cdot 2^2\cdot 3\\
\qquad (2^2)^2\cdot 3
\end{cases}\implies \sqrt{-1\cdot (2^2)^2\cdot 3}
\\\\\\
\sqrt{-1}\cdot \sqrt{(2^2)^2\cdot 3}\implies i\cdot 2^2\sqrt{3}\implies 4\sqrt{3}\ i$

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