Question

Prove that 9+7 root 3 is irrational

Answer 1

Answer: Let 9 +7 root 3 be rational.

Then, 9+ 7 root 3 = a/b (where a and b are co- prime and b is not 0)

7 root 3 = a/b-9        (Shifting 9 to right side)

root 3= (a/b-9)/7      (Shifting 7 to right side)

In this equation, (a/b-9)/7 is rational, on the other hand root 3 is irrational.

This is a contradiction. Hence our assumption is wrong.

So, 9+ 7 root 3 is irrational.

Hope it helps!!