Question

Classify the following number as rational or irrational:​$(3+\sqrt{23})-\sqrt{23}$

Answer 1

Given number is $(3+\sqrt{23})-\sqrt{23}$.

As $(3+\sqrt{23})-\sqrt{23}=3+\sqrt{23}-\sqrt{23}=3$

Now, $3$ can be written as $\frac{3}{1}$ which is in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$.

Hence, $(3+\sqrt{23})-\sqrt{23}$ is a rational number.