show that 5-2 root 3 is an irrational number
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Let us assume that 5-2√3 is rational
5-2√3 = p/q ( where p and q are co prime)
-2√3 = p/q-5
-2√3 = p-5q/q
-√3 = p-5q/2q
√3 = 5q-p/2q
now p , 5 , 2 and q are integers
∴ 5q-p/2q is rational
∴ √3 is rational
but we know that √3 is irrational . This is a contradiction which has arisen due to our wrong assumption.
∴ 5-2√3 is irrational
Step-by-step explanation:
Let us assume that 5-2√3 is rational
5-2√3 = p/q ( where p and q are co prime)
-2√3 = p/q-5
-2√3 = p-5q/q
-√3 = p-5q/2q
√3 = 5q-p/2q
now p , 5 , 2 and q are integers
∴ 5q-p/2q is rational
∴ √3 is rational
but we know that √3 is irrational . This is a contradiction which has arisen due to our wrong assumption.
∴ 5-2√3 is irrational