# Forgotten how to solve for square roots

#### Dustobusto

1. The problem statement, all variables and given/known data

compute f'(x) using the limit definition.

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

2. Relevant equations

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

3. 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.

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#### Mark44

Mentor
1. The problem statement, all variables and given/known data

compute f'(x) using the limit definition.

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

2. Relevant equations

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

3. 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

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