A root sign does not make a number irrational — √16 is 4. These free printable worksheets practice telling a rational root from an irrational one, perfect squares beside their neighbors.
If they get stuck
The answer key prints on a separate page.
√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 calls both irrational, so these sheets deal perfect squares and their close neighbors together — √49 and √48 look alike on the page and have opposite answers. Working the root out first is what settles it.
This is the roots-only cut of the rational-or-irrational sort, kept apart from the fractions, decimals and π that fill the mixed page, so the perfect-square misreading gets its own practice. A child does not have to compute √48 to answer — only to notice that 48 is not a perfect square, so its root never comes out and the number is irrational. Recognizing the perfect squares up to a few hundred is the real work.
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 roots, step by step