Question 44138
{{{sqrt(-4)}}} is not a real number. So the rule you mentioned is not applicable here.
Such numbers, with -ve sign under the radical, are called imaginery.
{{{sqrt(-1)}}} is called as the imaginery square root of unity and is denoted by {{{i}}}.
So, {{{i=sqrt(-1)}}}.
Hence, {{{i^2 = -1}}}.
Now, {{{sqrt(-4)}}} = {{{sqrt(4*(-1))}}} = {{{sqrt(4)*sqrt(-1)}}} = {{{2i}}}.
Hence, {{{sqrt(-4)*sqrt(-4)}}} = {{{2i*2i}}} = {{{4i^2}}} = -4


To know more about such problems read chapters on imaginery and complex numbers.
All the laws of Mathematical operation which hold for real numbers are not necessarily true with imaginery numbers.