Question

If root 2 is irrational prove that 7 minus 2 root 2 is irrational

Answer 1

Answer:

Step-by-step explanation

Lets assume 7-2$\sqrt{2$ to be rational

So,

7-2$\sqrt{2}$ = a/b    (Where a & b are co prime)

7-a/b = 2$\sqrt{2}$

7b-a/b = 2$\sqrt{2}$

7b-a/2b = $\sqrt{2}$

This is not possible coz we know that $\sqrt{2}$ is irrational

Hence our assumption was wrong and,

Therefore

7-2$\sqrt{2}$ is irrational

HOPE THIS HELPS YOU