Where would the number √2 lie on the number line?
between 1 and 2
We know that when a<b<c, then a2<b2<c2
Thus, the converse must be true. i.e., when a2<b2<c2, then a<b<c.
Now, we know that 1<2<4. Hence, √1<√2<√4 (When we consider the positive values of square roots)
Thus, 1<√2<2. Hence, √2 lies between 1 and 2.