Answer
The distance to the nearest stars is 5.0 light-years.
Work Step by Step
$b = \frac{L}{4\pi d^2}$
$d = \sqrt{\frac{L}{4\pi b}}$
Let $d_2$ be the distance to the nearest stars and let $d_s$ be the distance to the sun.
$\frac{d_2}{d_s} = \frac{\sqrt{\frac{L}{4\pi b_2}}}{\sqrt{\frac{L}{4\pi b_s}}} = \sqrt{\frac{b_s}{b_2}} = \sqrt{10^{11}}$
$d_2 = (\sqrt{10^{11}})(1.5\times 10^{11}~m)$
$d_2 = 4.74\times 10^{16}~m$
We can convert this distance to light-years.
$d_2 = (4.74\times 10^{16}~m)(\frac{1~ly}{9.46\times 10^{15}~m})$
$d_2 = 5.0~ly$
The distance to the nearest stars is 5.0 light-years.
