Question

if root of √3 is irrational prove that 5-2 √3 is irrational​

Answer 1

Answer:

5-2√3 is irrational .

Step-by-step explanation:

Let us assume that 5-2√3 is rational

then 5-2√3=p/q (where p and q are co prime

and q≠0)

-2√3=p/q-5

-2√3=p-5q/q

√3=p-5q/-2q

As we know √3 is irrational but p-5q/-2q is rational . A rational number is never equals to a rational number .

This contradiction has arisen because of our wrong assumption .

so 5-2√3 is irrational .

Hope it helps you .