what is the square root of -1

no I do not think so.

by the convention,     $$\sqrt{a\; number}\ge 0$$

 

for instance

 

$$\sqrt{25}=+5$$

 

even though    

 

  $$5^2=25\quad and\quad (-5)^2=25$$

$$\sqrt{-1}=i$$

 

i is NOT a real number it is an imaginary number.  It is the basic unit of the imaginary number system :)

actually,

the square root of -1 is ±1i