Find an integer a such that a < √ 77 < a + 1.
How should I go about this? I think 76 or 78 is possible but I have to pick to 1 and I'm not sure which.
Start by squaring the entire thing.
\(a^2 < 77 < (a+1)^2\)
Let's start with the first condition: a^2 < 77. From here, we know that a is equal to 8 or less.
Also, (8 + 1)^2 = 81, which works.
The integer a is 8.