I keep getting this question in my GCSE papers, but I have no idea how to solve it, and everywhere I look there doesn't seem to be a simple answer. The general question goes like this:
$v=\sqrt{\frac{a}{b}}$
$a = 6.43$ correct to 2 decimal places.
$b = 5.514$ correct to 3 decimal places.
By considering bounds, work out the value to $v$ to a suitable degree of accuracy.
(Sorry about the tagging, not sure what this fitted into)