#### Answer

3.873

#### Work Step by Step

Estimate $\sqrt {15}\approx4$
Divide the radicand by the approximation and average the divisor and quotient to refine the estimate.
$15\div4=3.75$
The average of 4 and 3.75 is $\frac{4+3.75}{2}=3.875$.
Repeat to further refine.
$15\div3.875=3.871$
The average of 3.875 and 3.871 is $\frac{3.875+3.871}{2}=3.873$.