Question 397869
{{{-2+sqrt(-100)}}}
With a negative number inside the square root, this expression represents a complex number. The first thing to do with this is write the square root in terms of "i", which is {{{sqrt(-1)}}}. So we factor out -1:
{{{-2+sqrt(-1*100)}}}
Then we use a property of radicals, {{{root(a, p*q) = root(a, p)*root(a, q)}}}, to write the square root of the product as the product of the square roots of the factors:
{{{-2+sqrt(-1)*sqrt(100)}}}
Not only does the {{{sqrt(-1)}}} simplify to "i", but {{{sqrt(100)}}} also simplifies to 10:
-2 + i*10
or
-2 + 10i