Question

Insert a rational number and an irrational number between $\sqrt{2}$ and $\sqrt{3}$.

Answer 1

Step 1. Find a rational number between $\sqrt{2}=1.414..$ and $\sqrt{3}=1.732...$

Rational numbers have terminating or non terminating and repeating decimals.

The rational number between $\sqrt{2}$ and $\sqrt{3}=1.58or\frac{158}{100}$

Step 2. Find an irrational number between $\sqrt{2}=1.414..$ and $\sqrt{3}=1.732...$

Irrational numbers are the numbers that do not terminate, nor do they repeat.

The irrational number between $\sqrt{2}$and $\sqrt{3}=1.57887888...$

Hence, $\frac{158}{100}$ is a rational number and $1.57887888...$ is an irrational number between $\sqrt{2}$ and $\sqrt{3}$.