Question

Where would the number $\sqrt{2}$ lie on the number line?

• A. between $0$ and $1$
• B. between $1$ and $2$
• C. between $2$ and $3$
• D. between $-1$ and $-2$

Answer 1

The correct option is B between $1$ and $2$

We know that $\sqrt{2}=\mathrm{1.4142....}$
and 1 < 1.4142 < 2
So, $\sqrt{2}$ lies between 1 and 2.

Alternatively if you don't know the value of $\sqrt{2}$, then
Consider 1, 2, 4.
We know that 1 < 2 < 4.
Take square root for all $⟹\sqrt{1}<\sqrt{2}<\sqrt{4}$
So, 1 < $\sqrt{2}$ < 2.
$\therefore \sqrt{2}$ lies between 1 and 2