Question

prove that 3πis rational or irrational​

Answer 1

Answer:

In the 1760s, Johann Heinrich Lambert proved that the number π (pi) is irrational: that is, it cannot be expressed as a fraction a/b, where a is an integer and b is a non-zero integer. In the 19th century, Charles Hermite found a proof that requires no prerequisite knowledge beyond basic calculus. Three simplifications of Hermite's proof are due to Mary Cartwright, Ivan Niven, and Nicolas Bourbaki. Another proof, which is a simplification of Lambert's proof, is due to Miklós Laczkovich.

Answer 2

Step-by-step explanation:

Let us assume on the contrary that 3 is a rational number.

Then, there exist positive integers a and b such that 3= ba

where, a and b, are co-prime i.e. their HCF is 1

Now,3 = ba

Hope its help..