$\sqrt{x}$ as an integer-valued fraction, when $x$ has an odd number of factors

Square Numbers and only square numbers have an odd number of factors. The square root of a square number is an integer. All integers are rational numbers. All rational numbers can be expressed as a fraction with integer components. Therefore the answer Yes is correct.

If we write down all numbers with an odd number of factors,
1, 4, 9, 16, 25, 36, 49, 64, 81, 100... We realise that they are all square numbers, meaning that $\sqrt{x}$ is always an integer, which can be interpreted as a fraction only using whole numbers.