#### Answer

3.465

#### Work Step by Step

Estimate $\sqrt {12}\approx3$
Divide the radicand by the approximation and average the divisor and quotient to refine the estimate.
$12\div3=4$
The average of 3 and 4 is $\frac{3+4}{2}=3.5$.
Repeat to further refine.
$12\div3.5=3.429$
The average of 3.5 and 3.429 is $\frac{3.5+3.429}{2}=3.465$.