#### Answer

7.071

#### Work Step by Step

Estimate $\sqrt {50}\approx7$
Divide the radicand by the approximation and average the divisor and quotient to refine the estimate.
$50\div7=7.143$
The average of 7 and 7.143 is $\frac{7+7.143}{2}=7.072$
Repeat to further refine.
$50\div7.072=7.070$
The average of 7.072 and 7.070 is $\frac{7.072+7.070}{2}=7.071$