Question

prove that 2/3-√3 is irrational.given root 3 is irrational

Answer 1

Answer:

Let 2+√3 is a rational number. A rational number can be written in the form of p/q. p,q are integers then (p-2q)/q is a rational number. ... Therefore,2+√3 is an irrational number.

Answer 2

Answer:

Hence Proved

Step-by-step explanation:

Let, 2/(3-√3) be a rational number.

so, 2/(3-√3) = p/q (where p and q are co-prime and q≠0)

2q = (3-√3)p

2q/p = 3-√3

-√3 = (2q/p) -3

√3 = 3-(2q/p)

since, 3,2,p and q are rational number so 3-(2q/p) will be rational.

That denotes √3 is rational but it is given that √3 is irrational.

So, it is contradicts √3 is irrational.

Hence, our assumption is wrong so, 2/3-√3 is irrational