# Limit of a squareroot combination.

1. Oct 9, 2009

### Dissonance in E

1. The problem statement, all variables and given/known data
find lim x---> infinity
sqrt(x + sqrt(x)) - sqrt(x)

2. Relevant equations
Conjugate multiplication.

3. The attempt at a solution
Ok so i know this is probably very easy yet it confuses me.
Im guessing youd need to multiply the numerator & denominator by the conjugate of the expression, and then work the expression into a form where all the x terms are denominators of a fraction so that as they approach inf, the fraction approaches 0.

(sqrt(x + sqrt(x)) - sqrt(x))(sqrt(x + sqrt(x)) + sqrt(x))
/ sqrt(x + sqrt(x)) + sqrt(x)

(x + sqrt(x) +sqrt(x)sqrt(x + sqrt(x)) -sqrt(x)sqrt(x + sqrt(x)) - x)
/ (sqrt(x + sqrt(x)) + sqrt(x))

sqrt(x)
/ (sqrt(x + sqrt(x)) + sqrt(x))

this is as far as i get, any help would be appreciated.

P.s: does this forum have a way of writing maths in a bit more easily comprehendable form?

2. Oct 9, 2009

### Dick

There should be a guide to using latex somewhere around here.

$$\sqrt{x+\sqrt{x}}=\sqrt{x} \sqrt{1+\sqrt{x}/x}$$

If you click on that it should pop up a window showing what I typed in. Sorry, I'm not all that good at it. By the way, that's your next step as well.

Last edited: Oct 9, 2009
3. Oct 9, 2009

### Dissonance in E

All right so we have:
sqrt(x)
/ (sqrt(x + sqrt(x)) + sqrt(x))

sqrt(x)
/ (sqrt(x) sqrt(1+sqrt(x)/x) + sqrt(x)

1 / sqrt(1+sqrt(x)/x) + 1

sqrt(x)/x tends to zero when x ---> infinity

1 / sqrt(1) +1

1/2

K that makes sense now, thank you.
And sry bout the lack of latex notation, il look into it for next time!