Step by step
The question
Question: is √12 rational or irrational?
Rational means: it can be written as a fraction, with whole numbers on top and at the bottom.
Then its decimal stops, or repeats for ever.
Irrational means: no fraction works.
Its decimal never stops and never repeats.
1 Look for a square number
Square numbers are a number times itself.
2 times 2 is 4.
3 times 3 is 9.
4 times 4 is 16.
12 is between 9 and 16.
So it is not a square number.
So √12 is not a whole number.
A calculator gives 3.4641, and so on.
The digits never stop and never repeat.
The square root of a whole number is either whole, or irrational.
Careful!
3.46 is only the rounded decimal.
It is close, but not exact.
So √12 is irrational.
Its decimal never stops and never repeats.
2 Check
Let's check: 3.46 times 3.46 is 11.9716, close to 12 but not 12.
More digits only get closer.
They never stop.
So the answer is right!
Let's look back.
First: look for a square number.
Last: check.