# square root using Taylor series

#### smslca

Joined May 11, 2009
26
As I am new to Taylor series, and im little confused, and in an urgent to expansion of sqrt
I want Taylor expansion for

$$sqrt{[(100*c)+21-p]^2-[8400*c]}$$
where "p" is constant. and "c" is variable.
and c>=1,

I need it in urgent.can anyone please expand it for me.

#### Papabravo

Joined Feb 24, 2006
15,537
The first requirement is that the function be infinitely differentiable around the point of expansion. Can you differentiate this function in some neighborhood? What point do you want the expansion to be around?

#### Redbelly98

Joined Jan 16, 2010
5
$$sqrt{[(100*c)+21-p]^2-[8400*c]}$$
What point do you want the expansion to be around?
Often, one of the terms under the radical is known to be significantly larger than the other(s). In those cases, you'd expand around that larger term -- either
[(100*c)+21-p]²​
or
[8400*c]
in this case.

(But if it's the latter term, we are in trouble!)