Question

How the answer would end in 15.81

Answer 1

$\bf \sqrt{250}\implies 15.\underline{81}138830084189665999 \\\\\\ \textit{to \underline{two} decimal places is just}\qquad 15.81$

so.... since the number after .81 is 1, it doesn't really round up to .82, so is just that, 15.81.