Question

Where would the number $\sqrt{5}$ lie on the number line?

• A. between 0 and 1
• B. between 1 and 2
• C. between 2 and 3
• D. None of the above

Answer 1

The correct option is B

between 1 and 2

We know that when $a<b<c$, then $a^2<b^2<c^2$ [if the number is greater than 1]
Thus, the converse must be true. i.e., when $a^2<b^2<c^2$, then $a<b<c$.
Now, we know that $4<5<9$. Hence, $\sqrt{4}<\sqrt{5}<\sqrt{9}$ [When we consider the positive values of square roots]
Thus, $2<\sqrt{5}<3$. Hence, $\sqrt{5}$ lies between $2$ and $3$.