Between what two consecutive integers do #sqrt310# lie?

1 Answer
Oct 14, 2015

Answer:

Between #17# and #18#.

Explanation:

I'd say that the simpliest way is just to go and try, of course with a little bit of wisdom.
For example, we know (or easily compute) that #10^2=100#, and #20^2=400#. So, #sqrt(310)# will surely be between #10# and #20#.

Now we narrow our search by confronting with midpoints: #15^2=225#, so #sqrt(310)# is between #15# and #20#.

Since #17^2=289#, #sqrt(310)# must be between #17# and #20#

But #18^2=324#, so #sqrt(310)# is exactly between #17# and #18#.

Of course, I solved the exercise using only confrontations and easy computing. One immediate way is simply to ask any calculator for #sqrt(310)#, he will give you back #17.6068...# and you'll immediately get the solution.