Question

rational number between root 2 and root4 ?

Answer 1

Task. Give an example of a rational number between $\sqrt{2}$ and $\sqrt{4}$.

Solution. In fact there are infinitely many rational numbers between any two distinct numbers $a<b$. For instance it is so for $a=\sqrt{2}$ and $b=\sqrt{4}$.

To give an example it suffices to find a rational number $q>0$ such that

$2<q^{2}<4,$

then

$\sqrt{2}<q<\sqrt{4}.$

Notice that

$2\ <\ 1.5^{2}=2.25\ <\ 1.6^{2}=2.56\ <\ 1.7^{2}=2.89\ <\ 4$

Therefore

$\sqrt{2}<1.5<1.6<1.7<\sqrt{4}.$

Thus we have found even 3 rational numbers between $\sqrt{2}$ and $\sqrt{4}$.

Answer. $1.5,1.6,1.7$.