What is √x squared?

[GrannySmith]

I am asking in regards to this function.

f(x) = √x + 3

I am supposed to find the x intercept, which you do by substituting 0 for f(x).

√x + 3 = 0
√x = 3

Could you not square both sides of the equation, and then get x = 9? Why doesn't this work algebraically?

 

[Deleted member 4993]

I am asking in regards to this function.

f(x) = √x + 3

I am supposed to find the x intercept, which you do by substituting 0 for f(x).

√x + 3 = 0
√x = -3 ..................... you should get a negative on the right hand side of the equation

Could you not square both sides of the equation, and then get x = 9? Why doesn't this work algebraically?

By definition,√x ≥ 0

Thus √x = -3 is not a valid solution.

 

[HallsofIvy]

I am asking in regards to this function.

f(x) = √x + 3

I am supposed to find the x intercept, which you do by substituting 0 for f(x).

√x + 3 = 0
√x = 3

You already have an error. Subtracting 3 from both sides gives \(\displaystyle \sqrt{x}= -3\). Since the square root is, by definition, non-zero there is NO value of x that satisfies that so there is NO x-intercept.

Could you not square both sides of the equation, and then get x = 9? Why doesn't this work algebraically?