Question 202898
It is difficult to know how to interpret "(-3 - radical -7)^2". If it does not mean {{{(-3 - sqrt(-7))^2}}} then please repost the question, using parentheses to make clear what you are try to say.<br>
If the problem is {{{(-3 - sqrt(-7))^2}}} then you must know about Imaginary numbers because if we are limited to Real numbers, we cannot allow {{{sqrt(-7)}}}.<br>
If {{{(-3 - sqrt(-7))^2}}} means {{{(-3 - sqrt(-7))*(-3 - sqrt(-7))}}}. If we multiply this out we get:
{{{(-3)^2 -2*(-3)*sqrt(-7) + (sqrt(-7))^2}}}
This simplifies to:
{{{9 - 6sqrt(-7) + (-7)}}}
and then
{{{-1 + (-6sqrt(-7))}}}
which is a complex number (a number with a Real part (-1) and an Imaginary part {{{-6sqrt(-7)}}}. We usually write Imaginary numbers interms of "i" which stands for {{{sqrt(-1)}}}. So we will take {{{-6sqrt(-7)}}} and factor out "i":
{{{-1 + (-6sqrt(-1*7)) = -1 + (-6sqrt(-1)*sqrt(7)) = -1 + (-6isqrt(7))}}}