According to the textbook context, the answer is a resounding NO. Numbers on the number line that cannot be expressed as a ratio of integers are called Irrational Numbers, and $\sqrt{2}$ is one such number. The proof of the irrationality of $\sqrt{2}$ uses the technique of Proof by Contradiction, showing that assuming $\sqrt{2}$ can be written as a rational number $\frac{p}{q}$ in its simplest form leads to a logical disaster where both $p$ and $q$ end up having a common factor of 2.