SOLUTION: I need help with: (-3 - radical -7)^2

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Question 202898This question is from textbook college algebra
: I need help with: (-3 - radical -7)^2 This question is from textbook college algebra

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
It is difficult to know how to interpret "(-3 - radical -7)^2". If it does not mean %28-3+-+sqrt%28-7%29%29%5E2 then please repost the question, using parentheses to make clear what you are try to say.

If the problem is %28-3+-+sqrt%28-7%29%29%5E2 then you must know about Imaginary numbers because if we are limited to Real numbers, we cannot allow sqrt%28-7%29.

If %28-3+-+sqrt%28-7%29%29%5E2 means %28-3+-+sqrt%28-7%29%29%2A%28-3+-+sqrt%28-7%29%29. If we multiply this out we get:
%28-3%29%5E2+-2%2A%28-3%29%2Asqrt%28-7%29+%2B+%28sqrt%28-7%29%29%5E2
This simplifies to:
9+-+6sqrt%28-7%29+%2B+%28-7%29
and then
-1+%2B+%28-6sqrt%28-7%29%29
which is a complex number (a number with a Real part (-1) and an Imaginary part -6sqrt%28-7%29. We usually write Imaginary numbers interms of "i" which stands for sqrt%28-1%29. So we will take -6sqrt%28-7%29 and factor out "i":