Question

use linear approximation to find an approximation of (square root of (145))^7

Answer 1

$(\sqrt{145})^7=(\sqrt{144+1})^7= [\ 12*\sqrt{1+1/144} \ )^7\\\\ = 12^7* [\ (1+\frac{1}{144})^{1/2}\ ]^7\\\\12^7*\ [ 1 +\frac{1}{144*2\ }\ ]^7=12^7 *\ [ 1 + \frac{7}{144*2}\ ]=12^7*\frac{295}{288}$