Hello. I am a high school teacher of Algebra. I was recently teaching square roots to my students and an interesting question arose. Our textbook seems to be inconsistent. I was hoping you might be able to give our department your opinion on who is correct as we are divided on the correct way to teach this. When you take the square root of a number, you get two answers, a positive root and a negative root, correct? Our book presents this as √4 = 2 and -√4 = -2 and ±√4 = ±2. Shouldn't it be taught as there are always two roots, the positive and the negative? It seems to me, there is really no reason to have to use the ± as there are always 2 roots, the positive and the negative. But if the negative sign is given then only the negative answer should be given? What's your take?
2 and -2 are both square roots of 4 since 22 = 4 and (-2)2 = 4. Thus, if the question is to find the square roots of 4, the answer is ±2. This can cause confusion if you want to specify one of the roots, either 2 or -2. To make this possible the surd symbol, √, is reserved for the positive square root. Thus if the question is to find √4 then the answer is 2. If you want to specify the negative square root then you can say -√4.