Explanation:
remember the definitions of these 2 types of numbers ?
rational numbers are all numbers that can be written as
a/b
where a and b are integers, and b <> 0.
this includes all real fractions, but also all whole or integer numbers, as they can be written as a/1.
if they have digits after the decimal point, they are either finite, or they have a repeating pattern for all eternity.
irrational numbers are all numbers with an infinite series of digits after the decimal point without any repeating patterns.
that includes all squares roots of non-squared numbers or any other roots of numbers that are not the product of correspondingly many multiplications with themselves. and trigonometric function and logarithm results, and the special numbers in math and physics : pi and e.
so,
4/7 is rational
sqrt(30) is irrational
21/sqrt(4) is a trick question, as sqrt(4) = 2.
so, this is actually
21/2 is rational
pi is irrational
-27 = -27/1 is rational