Question

Classify the following numbers as rational or irrational explain your reasoning3pie

Answer 1

An irrational number is a number which cannot be expressed as the quotient of two integers.

The constant:

`\pi`

Is an irrational number. So, the number:

`3\pi`

Must also be an irrational number. This is because if it was a rational number, then there would be two integers a and b such that:

`3\pi=(a)/(b)`

Then, we would be able to write the constant π as the quotient of a and 3b:

`\pi=(a)/(3b)`

which is not possible, since π is an irrational number.

Therefore, 3π is irrational.