- #1
brycenrg
- 95
- 2
Homework Statement
2-squareroot(16) = -2
Homework Equations
The Attempt at a Solution
Why is there not two answers? I thought the squareroot of something always has two answers.
brycenrg said:Homework Statement
2-squareroot(16) = -2
Homework Equations
The Attempt at a Solution
Why is there not two answers? I thought the squareroot of something always has two answers.
## \sqrt{b^2}=+b ##ShayanJ said:The square root is supposed to be a function, and a function is not allowed to give more than one output for a given input. So the convention is that ## \sqrt{b^2}=+b ##. .
Kaura said:Yeah there is the caveat when dealing with square roots in terms of functions that the absolute value or positive root is accepted as the output of the function
However you are correct that square roots typically have two solutions
I suppose it depends on the question or situation
a "square root" doesn't have a "solution" because a square root isn't a problem! A quadratic equation typically has two solutions.Kaura said:Yeah there is the caveat when dealing with square roots in terms of functions that the absolute value or positive root is accepted as the output of the function
However you are correct that square roots typically have two solutions
I suppose it depends on the question or situation
Yes.FactChecker said:It's the convention of the '##\sqrt {}##' symbol that it only means the positive value.
No, one should not always do this.FactChecker said:In practice, you should always put a '##\pm##' in front unless you have ruled out one of the values.
If there is a reason to rule one solution out, you should rule it out. Otherwise, all solutions should be considered. In this case, the absence of a '##\pm##' on the left side gives the reason to not consider the negative solution on the right side.Mark44 said:On the other hand, ##\sqrt 9 = 3##, and ##\pm## should not be used.
Mark44 said:On the other hand, √9=3, and ± should not be used.
As you said earlier, by convention the √ symbol denotes the positive value only. I hope you are not saying that there are circumstances in which, say, √9=±39=±3 would be correct.FactChecker said:If there is a reason to rule one solution out, you should rule it out. Otherwise, all solutions should be considered. In this case, the absence of a '±±' on the left side gives the reason to not consider the negative solution on the right side.
For the third time, no.Mark44 said:As you said earlier, by convention the ##\sqrt{}## symbol denotes the positive value only. I hope you are not saying that there are circumstances in which, say, ##\sqrt 9 = \pm 3## would be correct.
, which you quoted, and in your reply you saidOn the other hand, ##\sqrt 9 = 3##, and ##\pm## should not be used.
A simpler way to look at this is that ##\sqrt 9## simplifies to a single number.If there is a reason to rule one solution out, you should rule it out. Otherwise, all solutions should be considered. In this case, the absence of a '##\pm##' on the left side gives the reason to not consider the negative solution on the right side.
The square root of 16 is 4.
Solving for -2 in the square root of 16 means finding the number that, when squared, equals -2. In this case, the solution is imaginary, as there is no real number that, when squared, equals -2.
To solve for -2 in the square root of 16, we can rewrite the equation as sqrt(x) = -2 and then square both sides to get x = (-2)^2 = 4. However, since we are solving for a negative number, the solution is imaginary and can be written as 4i, where i is the imaginary unit.
No, the square root of 16 can never be a negative number. The square root of a number is defined as the number that, when multiplied by itself, equals the original number. Since a negative number multiplied by itself will always result in a positive number, the square root of 16 must be a positive number.
Explaining the steps when solving for -2 in the square root of 16 helps to show the reasoning and logic behind the solution and can help others understand and replicate the process. It also ensures accuracy and helps to avoid errors in the calculation.