Step by step
The question
Question: is √50 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.
6 times 6 is 36.
7 times 7 is 49.
8 times 8 is 64.
50 is between 49 and 64.
So it is not a square number.
So √50 is not a whole number.
A calculator gives 7.0710, and so on.
The digits never stop and never repeat.
The square root of a whole number is either whole, or irrational.
Careful!
7.07 is only the rounded decimal.
It is close, but not exact.
So √50 is irrational.
Its decimal never stops and never repeats.
2 Check
Let's check: 7.07 times 7.07 is 49.9849, close to 50 but not 50.
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.