## Prealgebra (7th Edition)

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 $\frac{8.063+8.062}{2}=8.063$.