Forgotten how to solve for square roots

[Dustobusto]

Homework Statement

compute f'(x) using the limit definition.

f(x) = $\sqrt{x}$

Homework Equations

f'(x) = $\stackrel{lim}{h→0}$ $\frac{f(x+h)-f(x)}{h}$

The Attempt at a Solution

Plugging in the function values gives you

f'(x) = $\stackrel{lim}{h→0}$ $\frac{\sqrt{(x+h)}-\sqrt{x}}{h}$

The end result is $\frac{1}{2\sqrt{x}}$ according to answer key.

I'm not sure how to go about solving. It's the square roots that are screwing me up. I have forgotten how to solve for square roots.

I've solved 6 problems within this context before coming across this one.

 

[Mark44]

Homework Statement

compute f'(x) using the limit definition.

f(x) = $\sqrt{x}$

Homework Equations

f'(x) = $\stackrel{lim}{h→0}$ $\frac{f(x+h)-f(x)}{h}$

The Attempt at a Solution

Plugging in the function values gives you

f'(x) = $\stackrel{lim}{h→0}$ $\frac{\sqrt{(x+h)}-\sqrt{x}}{h}$

The end result is $\frac{1}{2\sqrt{x}}$ according to answer key.

I'm not sure how to go about solving. It's the square roots that are screwing me up. I have forgotten how to solve for square roots.

I've solved 6 problems within this context before coming across this one.

Try multiplying by the conjugate over itself. IOW, multiply by
$$ \frac{\sqrt{x + h} + \sqrt{x}}{\sqrt{x + h} + \sqrt{x}}$$

 

[Dustobusto]

Understood. I got the answer now. Ty