One question decides it: can the number be written as a fraction of two whole numbers? These free printable worksheets ask it of roots, fractions, decimals and π.
If they get stuck
The answer key prints on a separate page.
A radical sign is not what makes a number irrational, and that is the misreading these sheets are built around. √2 is irrational; √16 is 4, which is as rational as a number gets. A child who has just met the word alongside the symbol will call both of them irrational, so the roots sheet deals perfect squares and their neighbors together — √49 and √48 look alike on the page and have opposite answers.
The decimals carry the mirror of the same mistake. 0.75 stops and 0.333… repeats, and both can be written as fractions, so both are rational. Only a decimal that neither stops nor repeats is not — which is why no question here shows a run of digits trailing off: eight places and an ellipsis could be the start of a repeating block nobody has reached, and the question would have no honest answer from the page.
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Rational or irrational, step by step