The square root of -1 does not have a 'real' value because
if a negative number is squared then the answer is positive and
if a positive number is squared the answer is positive too
SO no number squared equals a negative number!
There is another number system which include numbers that are not real. It is called 'The complex number system.'
It has imaginary numbers and sqrt(-1) is the base unit for the whole set of imaginary numbers.
In hre complex number system i is usually assigned the value of sqrt(-1), although very occasionally j is used instead.
I hope that helps :)