Classify the following numbers as rational or irrational explain your reasoning3pie

Question

asked May 22, 2023 225k views

1 Answer

Nazgul · Answer 1 · 2023-05-26T20:12:49+0000

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.