Is √2 rational or irrational

Step by step

The question

Question: is √2 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.

1 times 1 is 1.

2 times 2 is 4.

2 is between 1 and 4.

So it is not a square number.

So √2 is not a whole number.

A calculator gives 1.4142, and so on.

The digits never stop and never repeat.

The square root of a whole number is either whole, or irrational.

Careful!

1.41 is only the rounded decimal.

It is close, but not exact.

So √2 is irrational.

Its decimal never stops and never repeats.

2 Check

Let's check: 1.41 times 1.41 is 1.9881, close to 2 but not 2.

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.