Answer
67.61655
Work Step by Step
4624 is the closest perfect square to 4572
Let $a=68$
$y_{1}=1/2*(68+4572/68)$
$y_{1}=1/2*(68+67.235)$
$y_{1}=1/2*(135.235)$
$y_{1}=67.6176$
$y_{2}=1/2*(67.6176+4572/67.6176)$
$y_{2}=1/2*(67.6176+67.6155)$
$y_{2}=1/2*(135.2331)$
$y_{2}=67.61655$
