Prove that <msqrt>

Jayden Mckay

Jayden Mckay

Answered question

2022-05-14

Prove that 3 5 is irrational number.

Answer & Explanation

Athena Blanchard

Athena Blanchard

Beginner2022-05-15Added 13 answers

3 5 = ( m n ) 2
so 3 5 m 2 n 2 because 1 2 < 3 < 2 2 and 2 2 < 5 < 3 2
We may assume that g c d ( m , n ) = 1 and 3 n 2 = 5 m 2 . Since 3 5 m 2 we conclude that 3 m since 3 is prime. Hence 9 5 m 2 = 3 n 2 , so that 3 n 2 and hence 3 n. This is a contradiction to g c d ( m , n ) = 1.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?