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.
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.