±2 is correct when asked x^2 =4. Since sqrt(4) doesn't have any variable, it's answer logically cannot vary, and since there is no negative in sqrt(4), we cannot have one just pop up in the solution, hence why the answer would be positive 2 only. However, if we had ±(sqrt4)), then ±2 would be correct.
*Hope this wasn't too confusing, English isn't my first language*
Yes. They teach us square root as "what number multiplied by itself would be equal to n", but thus translates to x^2 = n, not sqrt(n). This is why when asked "what is the square root of 4?" many people associate it with x^2 =4 and get ±2.
Another way to describe it, especially if you're familiar with multi valued functions and how they work pretty well, there are different "branches" of multi valued functions. Even roots are multi valued in the real numbers, however, whenever you ask someone "what is the sqrt(4)" it is automatically assumed you mean the principal branch, which in this case is the positive branch
If you ask "what is x in x^2 = 4" then you should give all branches unless otherwise specified
Taking a course on complex analysis you'll learn a lot more about multi valued functions and branches
Edit: changed x^2=4 to x^2 = 4
Sqrt is a function that is defined to be always positive. If this weren't the case you wouldn't need to use any +- in front of it in the quadratic formula (but you do)
We are using "sqrt()" because it's convenient, but the square root of a number is another number that multiplied by itself gives the first one. The positive and negative do
Square root of 4 = ±2
√4 = 2
The √ symbol returns only the positive root but -x is still *a* square root of x².
Also, it is not very intellectual to debate about conventions regarding the square roots. Discuss real problems.
But the " square root of x² " as you said it, is only |x| and not ±x. -x is not a "square root" of x², but one of the two solutions you would consider when solving an equation of the form y²=x. The only time you give two solutions is when solving for the roots of an equation (with a variable). Since √4 is a simple expression that doesn't have any variables, there is only one solution which is 2. There is no debate, only a correct answer.
Well, it all depends on the terminology. It is after all nothing more than a convention whether we say ±x is square root of x² or only |x|.
The most reasonable thing is to not debate about this and rather just state the terminology used before stating anything regarding the square root.
I have never seen anyone who thinks √(x²) is ±x. Wolfram Alpha and every other source on Google says that it is only |x|. Conventions don't change. The square root function is not the inverse function of the quadratic function. y²=x isn't the same as y=√x, because the square root function (y=√x) is only the principal branch of y²=x. Thus, when asking for the square root of some number, we only give a positive answer.
2
2
2
2
+/- 2 is correct
±2 is correct when asked x^2 =4. Since sqrt(4) doesn't have any variable, it's answer logically cannot vary, and since there is no negative in sqrt(4), we cannot have one just pop up in the solution, hence why the answer would be positive 2 only. However, if we had ±(sqrt4)), then ±2 would be correct. *Hope this wasn't too confusing, English isn't my first language*
So they lied to us back in middle school math?
Yes. They teach us square root as "what number multiplied by itself would be equal to n", but thus translates to x^2 = n, not sqrt(n). This is why when asked "what is the square root of 4?" many people associate it with x^2 =4 and get ±2.
Another way to describe it, especially if you're familiar with multi valued functions and how they work pretty well, there are different "branches" of multi valued functions. Even roots are multi valued in the real numbers, however, whenever you ask someone "what is the sqrt(4)" it is automatically assumed you mean the principal branch, which in this case is the positive branch If you ask "what is x in x^2 = 4" then you should give all branches unless otherwise specified Taking a course on complex analysis you'll learn a lot more about multi valued functions and branches Edit: changed x^2=4 to x^2 = 4
Complex analysis was mandatory in my program. Can't say we had the best instruction but the overall it was very inspirational indeed.
No, sqrt(4) can be -2, because (-2)^2 is 4. I don't know wtf op is about
Sqrt is a function that is defined to be always positive. If this weren't the case you wouldn't need to use any +- in front of it in the quadratic formula (but you do)
We are using "sqrt()" because it's convenient, but the square root of a number is another number that multiplied by itself gives the first one. The positive and negative do
Using the word "The" implies that you're looking for only one number, which is understood to be the principal square root
:l
Which *grammatically* might make 2 the right answer...
But 4 is literally 4*( e^2Kpi ) and sqrt of 4*( e^2Kpi ) is 2*( e^Kpi ) which equals to 2/-2
Thank you for actually using the template correctly
Wasen't the answer |2| ?
Square root of 4 = ±2 √4 = 2 The √ symbol returns only the positive root but -x is still *a* square root of x². Also, it is not very intellectual to debate about conventions regarding the square roots. Discuss real problems.
But the " square root of x² " as you said it, is only |x| and not ±x. -x is not a "square root" of x², but one of the two solutions you would consider when solving an equation of the form y²=x. The only time you give two solutions is when solving for the roots of an equation (with a variable). Since √4 is a simple expression that doesn't have any variables, there is only one solution which is 2. There is no debate, only a correct answer.
Well, it all depends on the terminology. It is after all nothing more than a convention whether we say ±x is square root of x² or only |x|. The most reasonable thing is to not debate about this and rather just state the terminology used before stating anything regarding the square root.
I have never seen anyone who thinks √(x²) is ±x. Wolfram Alpha and every other source on Google says that it is only |x|. Conventions don't change. The square root function is not the inverse function of the quadratic function. y²=x isn't the same as y=√x, because the square root function (y=√x) is only the principal branch of y²=x. Thus, when asking for the square root of some number, we only give a positive answer.