The answer is what you make of it. The radical symbol on its own means nothing; it is a shape of lines only.

The phrase "square root" also doesn't mean anything based on the words making it up.



A message conveyed between two people through a medium such as a language of words or symbols does not have intrinsic meaning derived from the way it is represented in the medium. The sender and receiver interpret what the message is SUPPOSED to mean, and that's all a meaning is.



The letter A does not mean anything except a component of words or an article to most people, but if a teacher sends the letter A to a student on a sheet of paper which was previously submitted by the student as an assignment, the teacher and the student both take the letter to mean that the student has done well.



If one who does not speak English is told that his shirt is on backwards (just giving a random example here), he might think it was a friendly compliment and feel happier for the day. It didn't mean the same thing to the non-English-speaker as it meant to the English-speaker.



This can be applied to the concept of the radical sign and the term "square root". It doesn't always mean the same thing to different people. An authority figure could say that it means something to him, and this meaning could be widely accepted, but it might not be universally accepted. The meaning of the operation is what it is thought to be by the person using it.



Therefore, if someone believes that the square root operation means only the principal root (the positive answer), and that this operation is therefore a function, he would be correct in saying it means that to him. If someone believes that the square root operation means the inverse of squaring, so it means the positive and negative root, he would also be correct in saying it means that to him.



But no one can say it means something by virtue of itself. It represents a concept to those who interpret it to do so. On an alien planet, square root might not mean anything at all. On an alien planet, square root might mean an obscenity. It can mean whatever it is believed to mean.



I believe the principal square root and the other square root are two DIFFERENT operations, therefore, and depending on context and what I think the writer of the operation intended, I could take "square root" or the radical symbol to mean either operation.



I put this under the YES column only because it had to be under a column, and because it only asked if the square root CAN be -1. It CAN mean that. That doesn't mean the NO column people are wrong. Report Post

-1 x -1=1 When asking this question, you need to consider what a square root is. Well, the square root of a number is whatever is multiplied by itself to get that number. Basically, the sq. Rt. Of a = b*b. 1= -1*-1 is a true statement, so -1 is a square root of 1. It doesn't matter if we want it to be a function. -1 is still a solution to the square root of 1 Posted by: JayFortner Report Post

Really Makes Sense Negative One Multiplied By Negative One Equals To One So Ummmmmmm Ya....... I Guess, I Have Never Of This But When i Hear It. What Pops in my mind is that its Correct, So My Question Is The Square root of 4 Possible to Be -2?

I'm really Confused..... But I support it!

:) Posted by: Terryhawk Report Post

This is a mathematical fact. Since -1 squared equals 1, it is necessarily true that -1 is a square root of 1. The other square root is 1. It would be most accurate to say that -1 is "a square root of 1" rather than it is "the square root of 1". I think that would be the only room for debate here, except the question as asked is "can the square root of 1 be -1". It can be, but it can also be 1. Posted by: ronarprfct Report Post

Is this a serious question? Squaring a number is simply taking a number and multiplying it by itself. So when you find a square root of an number you are looking for a the same number that can be multiplied together to get what is being square rooted. So when you take the number 1 and find the square root of it you can either have 1 times 1 or -1 times -1. The reason you can have a a negative for the square root of one is because the two negatives cancel one and other out which creates a one. Posted by: CFS Report Post

Obviously, This is a fact (most)every number has two square roots, One positive and one negative. -1*-1=1, So yes. It is a square root. 1*1=1 as well, So the two square roots of 1 are -1 and 1. Come on people, I am 12 years old. This is not that hard to understand because one negative number times another negative number equals a positive number. Report Post

√1 equals both 1 and -1. The use of the square root is to find the one number that when multiply to each other, Gets the number under the radical symbol.

√25=5, -5 because 5(5)=25 and -5(-5)=25.

When doing all square roots or any radicals with an even index, It is important to include the plus or minus (±) symbol.

So by definition, √1=±1. Most graphs and calculators only focus on the principal root, Where they only deal with the non-negative numbers. But according to algebra, Especially in quadratics, The ± is very important. For example:

(x^2)-4=0

(x^2)=4

x=±2



(x^2)-4=0

(x+2)(x-2)=0

x=-2, X=2



By all these examples, √1 can equal to -1. Report Post

Ahh, Algebra Skills The square root of 1 can be -1 because (-1)(-1)=1, And so does 1. But if we are talking about principal root, Then the answer is 1 only. Remember, Any radical with an even index will have a positive and negative answer. It is just the basis of algebra.

Note: Most graphing calculators only graph principal roots, As it is much more easier to deal with only the positive than the negative. Report Post

Guys I don't think any of you know what you're even talking about First of all, the square roots are the inverses to squares. If a^2 = c, then √c = a.



We define √c to be equal to a, where a^2=c. It's just that √c has multiple solutions, a and -a.



So √1 = 1, and √1 = -1. There's no denying it. Both 1 and -1 are solutions to the equation x^2 = 1. In this case, 1^2 = 1 and (-1)^2 = 1. Nothing more, and nothing less.



The reason why we only use the positive values, is not because there's anything mathematical about it, but because it's just our human convention. We just like positive values. Posted by: ChaoticMC Report Post