In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. For example, 4 and −4 are square roots of 16 because 4² = ( − 4 )² = 16.
Edit: I’m wrong lol, there is a difference between the square root function, which accepts two results, and the square root, or principal square root, which is a unique positive number
So close yet so far. If only you had read ONE more paragraph.
Every nonnegative real number x has a unique nonnegative square root, called the principal square root or simply the square root (with a definite article, see below), which is denoted by √x where the symbol “√” is called the radical sign or radix.
This sentence made no sense to me as it directly contradicted the previous one. But it’s just a confusion on my part between the function called square root, which confusingly outputs two different numbers called “square roots”, and “the” number called square root; I’ve edited my comment. Thanks for correcting me!
Yeah, I see how that can happen. Very confusing to have the same name for two things differentiated only by the use of a definite or indefinite article.
You can get the sqrt of a given y by looking at the x axis. E.g. the value of y=4 has two solutions, x=2 and x=-2. This however does not mean that the sqrt of -4 is also 2! If you look at graph you can see that there are no solutions for y less than 0.
sqrt(-1) , sqrt(-2) (i ill omit imaginary numbers here) and so on do not have a solution. There is nothing you can replace with such that x × x is < 0 because multiplying two negatives always nets a positive.
Don’t know why you are being down voted. You are correct. There is a difference between a square root and the solutions of x2 = n.
Yeah, square root implies absolute numbers. You need to manually multiply by -1 to get the other solution to x^2
No?
Wikipedia
Edit: I’m wrong lol, there is a difference between the square root function, which accepts two results, and the square root, or principal square root, which is a unique positive number
So close yet so far. If only you had read ONE more paragraph.
This sentence made no sense to me as it directly contradicted the previous one. But it’s just a confusion on my part between the function called square root, which confusingly outputs two different numbers called “square roots”, and “the” number called square root; I’ve edited my comment. Thanks for correcting me!
Yeah, I see how that can happen. Very confusing to have the same name for two things differentiated only by the use of a definite or indefinite article.
Look at the inverse of the square root function, f(x)=x² (https://www.desmos.com/calculator/2v5gzbhru8)
You can get the sqrt of a given y by looking at the x axis. E.g. the value of y=4 has two solutions, x=2 and x=-2. This however does not mean that the sqrt of -4 is also 2! If you look at graph you can see that there are no solutions for y less than 0.
sqrt(-1) , sqrt(-2) (i ill omit imaginary numbers here) and so on do not have a solution. There is nothing you can replace with such that x × x is < 0 because multiplying two negatives always nets a positive.
I really don’t like the sqrt shorthand.
They knew.