# Thread: Use of differentials to approximate

1. ## Use of differentials to approximate

use differential to approximate Square root 17.

2. Originally Posted by av8or91
use differential to approximate Square root 17.
Have you tried anything here?

3. I know we need to do something with the closes square root which is 16. I just can remember how to do the rest.

4. Originally Posted by av8or91
I know we need to do something with the closes square root which is 16. I just can remember how to do the rest.
use $\displaystyle f(x + \triangle x) \approx f(x) + f'(x) \triangle x$ with $\displaystyle f(x) = \sqrt{x}$

5. Im still not 100 percent getting this. Could someone show me how to do it? Thanks

6. $\displaystyle \sqrt{17}=f(x+\Delta x)$
Where $\displaystyle x=16$, $\displaystyle \Delta x=1$, and $\displaystyle f(x)=\sqrt{x}$

$\displaystyle f(x+\Delta x)\approx f(x)+{f}'(x)\Delta x$

$\displaystyle {f}'(x)=\frac{\mathrm{d}[\sqrt{x}]}{\mathrm{d} x}=\frac{1}{2\sqrt{x}}$

$\displaystyle f(17)\approx f(16)+(1){f}'(16)=4+\frac{1}{8}=33/8=4.125$

I hope this helps.