Algebra: Rational & Irrational Numbers Unit test:

Question

Proven that the product of 2π and 3/4 is an irrational number. Find the product and explain why the value is irrational. Explain your reasoning in 1 sentence.

Answer 1

The product of \(2\pi\) and \(\frac{3}{4}\) is

\[ 2\pi \times \frac{3}{4} = \frac{3\pi}{2}. \]

Since \(\pi\) is an irrational number, and the product of a non-zero rational number (\(\frac{3}{2}\)) and an irrational number (\(\pi\)) is always irrational, \(\frac{3\pi}{2}\) is irrational.