Step by step
The question
Question: is √20 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.
3 times 3 is 9.
4 times 4 is 16.
5 times 5 is 25.
20 is between 16 and 25.
So it is not a square number.
So √20 is not a whole number.
A calculator gives 4.4721, and so on.
The digits never stop and never repeat.
The square root of a whole number is either whole, or irrational.
Careful!
4.47 is only the rounded decimal.
It is close, but not exact.
So √20 is irrational.
Its decimal never stops and never repeats.
2 Check
Let's check: 4.47 times 4.47 is 19.9809, close to 20 but not 20.
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.