Question

A cube has a volume of 800 cubic units. the length of the edge of this cube is between which two numbers?

Answer 1

I set this up as an inequality, $800 \leq s^{3}$.  If you take the cubed root of 800, you get the lower bound of the side length, which is 9.2.  Then I just worked my way up until I hit the first number that put me over a volume of 800.  That number is 9.29, because 9.28 cubed is 799.1 (not high enough) and 9.29 cubed is 801.8.  Therefore, the bounds of the sides exist within a conjunction: $9.2\ \textless \ s\ \textless \ 9.29$.  That's the best I could come up with to help on that one.  Wasn't sure if there was another method you were taught at school. I just used common sense more than any rule.