The idea here for estimating square roots is to pin the number under the radical (2 in this case) between two perfect squares.
2 is between 1 and 4.
sqrt(1) = 1 and sqrt(4) = 2.
Since 2 is between 1 and 4, sqrt(2) is between sqrt(1) and sqrt(4).
This means sqrt(2) is between 1 and 2.