Ok our lecturer asked the question if we knew WHY the square of 2 real numbers is always positive.

I know the simple rules we learned at school like the product 2 different signs always make a positive and the product of 2 matched signs always make a positive and the idea that the two negative statements make a positive (eg I don't know nothing = I know something) but I have never learned why this is so.

Ive looked around on the net a lot but can't find anything that satisfies me (its all aimed at high school students).

Thanks for the help and I hope this is the right sub-forum haha.

Ryan

One thing I can think of is that the square root of a negative number is a complex number but that doesn't really help me in seeing the question asked. (Its not an assignment question by the way...I'd never cheat like that)