# Thread: First 25 digits after decimal point of (sqrt(10)+5)^100?

1. ## First 25 digits after decimal point of (sqrt(10)+5)^100?

How would you go about finding the first 25 digits after decimal point of $(\sqrt{10}+5)^{100}$? (without using calculator)

2. To begin with

$
(1+x)^{1/2}=1+\frac{1}{2}x-\frac{1}{8}x^2+...
$

$
(1+9)^{1/2}=3(1+\frac{1}{9})^{1/2}=...
$

You must evaluate number of terms needed for this accuracy.

The same with

$
(1+x)^{100}=...
$