#### Answer

8.063

#### Work Step by Step

Estimate $\sqrt {65}\approx8$
Divide the radicand by the approximation and average the divisor and quotient to refine the estimate.
$65\div8=8.125$
The average of 8 and 8.125 is $\frac{8+8125}{2}=8.063$.
Repeat to further refine.
$65\div8.063=8.062$
The average of 8.063 and 8.062 is $\frac{8.063+8.062}{2}=8.063$.