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Q: How do you know if a number is irrational?

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If a number can be expressed as a fraction then it is rational if not then it is irrational.

It is proven that between two irrational numbers there's an irrational number. There's no method, you just know you can find the number.

The answer to this question confuses me. The square root of two is an irrational number, so obviously if the square root of two is squared it becomes two which is a rational number. Thinking of it that way then the answer is yes, the square of an irrational number can be a rational number. But . . . You had to know beforehand that the irrational number was the square root of another number. If you start out with an irrational number such as Pi you cannot square it because you cannot know the entire number in order to square it.

Pi is an irrational number. Johann Heinrich Lambert proved that in the late 18th Century.

No. The sum of an irrational number and any other [real] number is irrational.

The sum of a rational and irrational number must be an irrational number.

It is always rational.

rational * irrational = irrational.

No, 3.56 is not an irrational number. 3.56 is rational.

No. this is not a irrational number

It is not an irrational number!

A negative irrational number can be thought of as an irrational number multiplied by -1, or an irrational number with a minus sign in front of it.

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