square roots of -100

square roots of -100

$\begin{array}{|rcll|} \hline && \sqrt{-100} \\ &=& \sqrt{ 100\cdot (-1)} \\ &=& 10 \cdot \sqrt{ -1 } \\ &=& 10 \cdot \sqrt{ -1 } \quad & | \quad \sqrt{z} = \sqrt{-1+0\cdot i} = \sqrt{-1} = \pm i \\ &=&10 \cdot (\pm i) \\ &=&\pm i\cdot 10 \\ \hline \end{array}$

it will be +10i or -10i

it is impossible to have a real number as a square root of a negative number