Answer
12.53
Work Step by Step
$\sqrt {157}$ is between $\sqrt {144}=12$ and $\sqrt {169}=13$
Divide by one of the square roots, then average:
$157\div12=13.08\overline3$
$(12+13.08\overline3)\div2=12.541\overline6$
Repeat:
$157\div12.542=12.518$
$(12.542+12.518)\div2=12.53$
