The definition of a square root is " a number which when squared has the target value."
In this case it is any number which when squared gives 2b.
For square roots there are always two possibilities. Because there are always two different numbers that can answer the definition.
-8 * -8 = 64
which would make -8 a possible square root of 64.
8 * 8 also makes 64 so that is also a possible square root of 64
Which means that the square root of 64 may be either -8 OR +8 and we cannot know which one is true unless there is some physical reason why one is preferred over the other. They are both equally valid.
In EITHER case however we get 2b = 64 and b = 32
In other words sqrt( 2b) = 8 or sqrt ( 2b) = -8 both have the same solution
b= 32
And whomsoever put the thumbs down on the other answers. The three I have seen are all correct.
It's possible in this equation, because sqrt(64) has two answers, 8 and -8.
However, you might be confused because the function f(x) = sqrt(2x) can never be negative. This is because functions are defined such that for every value you plug in to the independent variable, x, there can be no more than one resulting value for the dependent variable, f(x). Though it seems by convention, they decided to use the positive half to represent sqrt(x) rather than the negative half. For the negative half, you would have to explicitly say -sqrt(x).
It wouldn't be the same if x was the dependent variable, and y was the independent variable, where y = sqrt(2x). In this case, you can solve for x to get x = y^2/2. This is perfectly fine, because the result is a parabola openning in the x-direction, and there aren't any values of y that you can input that could result in more than one x value. The domain of x, which is the range of possible values that its independent variable, y, can take, is all real numbers.
So whether we're working with functions, or just regular equations affects how things work.
Since in the set of real numbers (our number system) there is a mathematical rule saying it is impossible to get a negative value from a square....
This is because neg * neg = positive
So in the set of real numbers it is impossible... However, later you learn about the complex numbers which i dont know for sure... but my teacher touched on it... But i do know how to solve your problem...
In the Complex Number System the letter 'i' is represented asâ-1... this means we can go like this...
2b=64
b=32 right?
But here you add the letter 'i' beside it to represent â-1...
so therefore, b = â1024 * i <----- (32*32=1024, that means â1024 = 32) in a set of complex numbers
My understanding is the square root symbol you used actually indicates the principal AKA positive square root, so that equation would not be true, but if you are taking the general square root, then sure it can be negative. You can't find a real square root of a negative, but squaring a negative gives a positive. b would be 32.
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Verified answer
root(2b)=-8
=> 2b = (-8)^2 =64
=> b = 32
remember square of real numbers are not negative but sqrt can always be negative.
The definition of a square root is " a number which when squared has the target value."
In this case it is any number which when squared gives 2b.
For square roots there are always two possibilities. Because there are always two different numbers that can answer the definition.
-8 * -8 = 64
which would make -8 a possible square root of 64.
8 * 8 also makes 64 so that is also a possible square root of 64
Which means that the square root of 64 may be either -8 OR +8 and we cannot know which one is true unless there is some physical reason why one is preferred over the other. They are both equally valid.
In EITHER case however we get 2b = 64 and b = 32
In other words sqrt( 2b) = 8 or sqrt ( 2b) = -8 both have the same solution
b= 32
And whomsoever put the thumbs down on the other answers. The three I have seen are all correct.
It's possible in this equation, because sqrt(64) has two answers, 8 and -8.
However, you might be confused because the function f(x) = sqrt(2x) can never be negative. This is because functions are defined such that for every value you plug in to the independent variable, x, there can be no more than one resulting value for the dependent variable, f(x). Though it seems by convention, they decided to use the positive half to represent sqrt(x) rather than the negative half. For the negative half, you would have to explicitly say -sqrt(x).
It wouldn't be the same if x was the dependent variable, and y was the independent variable, where y = sqrt(2x). In this case, you can solve for x to get x = y^2/2. This is perfectly fine, because the result is a parabola openning in the x-direction, and there aren't any values of y that you can input that could result in more than one x value. The domain of x, which is the range of possible values that its independent variable, y, can take, is all real numbers.
So whether we're working with functions, or just regular equations affects how things work.
Since in the set of real numbers (our number system) there is a mathematical rule saying it is impossible to get a negative value from a square....
This is because neg * neg = positive
So in the set of real numbers it is impossible... However, later you learn about the complex numbers which i dont know for sure... but my teacher touched on it... But i do know how to solve your problem...
In the Complex Number System the letter 'i' is represented asâ-1... this means we can go like this...
2b=64
b=32 right?
But here you add the letter 'i' beside it to represent â-1...
so therefore, b = â1024 * i <----- (32*32=1024, that means â1024 = 32) in a set of complex numbers
sqrt(i^4 2*32) = i^2 sqrt(64) = - 1*8 = - 8. So b = i^4 32 ANS.
i is an imaginary number which yields by definition i^2 = - 1.
â(2b)=-8
(2b) = -8² = 64
b = 32
My understanding is the square root symbol you used actually indicates the principal AKA positive square root, so that equation would not be true, but if you are taking the general square root, then sure it can be negative. You can't find a real square root of a negative, but squaring a negative gives a positive. b would be 32.