Re-asked: √x-2 + √x+3 ?

Question

Re-asked:  √x-2 + √x+3 ?

anonymous · Answer

Add like terms

anonymous · Answer

So it just becomes 2x +1?

anonymous · Answer

|dw:1347502863124:dw|

anonymous · Answer

Why not over it all, the sqrt is supposed to be covering the whole thing?

anonymous · Answer

So, do you mean:
$$
\sqrt{x-2}+\sqrt{x+3}
$$?

anonymous · Answer

Yeah

mathslover · Answer

$$\sqrt{x-2}+\sqrt{x+3}$$?

anonymous · Answer

You cannot simplify this further. Not directly, at least.

mathslover · Answer

square both sides by letting rhs be n

anonymous · Answer

Thats it...... nothing can be done. thats the simplified form

mathslover · Answer

squaring?

anonymous · Answer

But there has to be a way, this a question for my test review?

mathslover · Answer

square it

anonymous · Answer

No, you could do difference of squares, but you'd have to divide again. There's literally no other simplifications.

mathslover · Answer

hmn right

anonymous · Answer

The answer in the answer bank was [2,infinity), I think the end result should be the domain...?

anonymous · Answer

Okay, that makes more sense, then.

anonymous · Answer

We have that to make sure that $\sqrt{x}$ is real, $x>0$. Which means that:
$$
x-2>0\implies\
x>2
$$And:
$$
x+3>0\implies\
x>-3
$$Since, we have one more strict condition, we take the former, and so, we get
$$
x\in[2,\infty)
$$

anonymous · Answer

Oh I get it now, it has to be > than 0. Thanks a lot, really helped.

anonymous · Answer

Sure thing.