Question

$\sqrt{2}$ lies between on the number line.

• A. 0 and 1
• B. 1 and 2
• C. 2 and 3

Answer 1

Answer: (A), (B)

1 and 2

We know that when $a<b<c$, then $a^2<b^2<c^2$.

Thus, the converse must be true. i.e., when $a^2<b^2<c^2$, then $a<b<c$.

Now, we know that $1<2<4$. Hence, $\sqrt{1}<\sqrt{2}<\sqrt{4}$ (When we consider the positive values of square roots).
Thus, $1<\sqrt{2}<2$.

Hence, $\sqrt{2}$ lies between $1$ and $2$.