and so, if you have the principal square root of a times the principal square root of b, that's the same thing as square root a times b so based on this property of the radical of the principal root, they'll say this over here is the same thing as the squrae root of negative 1 times negative 1 if i have the principal root of the product of 2 things that's the same thing as the the product of each of their principal roots i am doing this in other order here. here i had the principal root of the products, over here i have this on the right and then from that we all know that negative 1 times negative 1 is 1 so this should be equal to the principal square root of 1 and then the principal squre root of 1, remember this radical means principal squre root, positive squre root that is just going to be positive 1 and they'll say this is wrong. clearly negative 1 and positive 1 are not the same thing and therefore you can't make the subtitution that we did in this step and you should then point out is that, this was not the incorrect step that it is true that negative 1 is not equal to 1 but the faulty line of reasoning here was in using this propperty when both a and b are negative, if both a and b are negative this will never be true, so a and b both can not be negative infact normaly when this property is given, sometimes is given a little bit in footnotes you might not even notice it because its not relevant when you