No, #sqrt13 # is an infinite non-recurring decimal. 13 is not a perfect square and therefore does not have an exact square root.
It is an irrational number, along with numbers such as #pi, sqrt20, sqrt 33, sqrt8, e, etc#
#sqrt13# cannot be written as a ratio of integers and as a result cannot be written as a fraction, which is the definition of a rational number.
Rational numbers include the Integers (positive and negative whole numbers) the fractions, and all the terminating and recurring decimals.
#3/4, -26, 11/3, 2/9, 3 5/8, -204, etc#