Kati Hi. My idea is not to be found as an expert... Yeah I agree with the errors, but this is a comment section not an exposé so I didn't pay much attention to that I thank you for pointing it out. Second, no need to be that aggressive. Simply point how where I explained wrongly and why. Third as Niki said, I was coming from a pov of x^2=a (where in the above case x=a) and try to make it correct. Ofc stating that sqrt(a^2) = abs(a) is also a way to do it. Next time try to be less condescending. No one should feel bad by sharing their pov and be corrected afterwards. That's how we learn =) I deleted the comment so you can explain as you wish. I seriously do not have the patience to deal with this.

exccept they don't, sqrt(a^2)=abs(a), in this case 1=sqrt((-1)^2)=abs(-1)=1, what you are saying is correct for an equation of the form x^2=a, where the solution for x would be sqrt(a) as well as - sqrt(a), where again the actual value for sqrt(a) is always positive, which you can also verify by looking at the graph for the fuction f(x)=sqrt(x)

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Tiago, I'm sorry, but your explanation is full of mistakes and I can't let that stay incorrected :D) becoming a math - teacher)... So in the first equation it has to be (-3)^2=(3)^2=9 ... Not sqrt(9). And in the second one (I assume you mean ^ instead of *) what you are saying is, that 1=+/- 1... Not correct. What you tried so say, is probably that 1= |sqrt ((-1)^2)|,... Could also be (1^2), doesn't matter... Could also be sqrt(1),to point out the right thing. Because the sqrt is essential. Because sqrt(1) is +/- one. That's the deal behind it... You'r sounding like an expert, but in the end it's actually completely wrong. Like... Think twice, before you think you are right, because sry, but your comment is no better then all the examples in this post.

The square root of 1 is 1 and -1.. There are always two answers to a square root. (for 9 it's 3 and -3, for 100 it's 10 and -10 and so on)

The error lies in the people trying to correct this...

Alex: Actually, no. The square root function can use two negative or two positive numbers, since multiplying two negative numbers always results in a positive number. That's the deal, here: in multiplying numbers, only when one is negative and the other is positive is the answer negative. The other part of the problem is the nomenclature: if you want to show negative numbers with any power, like -1 (squared), you do what sonofabass said: use parentheses. Or, how Alexander S put it: show +/-1. (The plus is above the minus, with the number to the right.) Whoever did this understands square roots, but not imaginary numbers and how we get them.

You asked to be corrected, so I'll reply again directly to you so you can see. :) The square root is always "plus or minus". Since 1 squared and -1 squared are both 1, and 2 squared and -2 squared are both 4, square root of 1 is properly ±1 and square root of 4 is properly ±2.

Why y'all downvoting? I didn't know that so it was helpful aight? Just don't be rude please. I'm praying for y'all btw with the corona an all. Stay safe Les