Question

Find the irrational number between $2$ and $2.5$.

Answer 1

Find the irrational number between the given numbers

Given numbers: $2$ and $2.5$.

We know that, irrational numbers are those which cannot be expressed in the form of $\frac{a}{b}$ where $b\ne 0$

For example: $\sqrt{2}$ and $\sqrt{3}$ are irrational numbers.

We also know that, if $a$ and $b$ are two distinct positive rational numbers which is not a perfect square then the irrational number $\sqrt{ab}$ lies between $a$ and $b$.

As $2$ and $2.5$ are two distinct positive rational numbers which is not a perfect square.

So, the irrational number between $2$ and $2.5$ is $\sqrt{2\times 2.5}=\sqrt{5}$.

Hence, the irrational number between $2$ and $2.5$ is $\sqrt{5}$.