please explain with words
Let x= sqrt6+ sqrt7 . What two consecutive integers does x lie between? Figure out the answer without using a calculator.
Explain in words how you arrived at your answer, and how you know for certain that it's correct. (Imagine that you are trying to convince a very skeptical person of this; a guess won't cut it.)
Note that sqrt (4) = 2 and sqrt (9) = 3
sqrt (6) and sqrt (7) must both lie between 2 and 3
So....the most that sqrt (6) + sqrt (7) can be is 3 + 3 = 6
So..... this sum must lie between 5 and 6