Question

Prove that $7-4\sqrt{2}$ is irrational.

Answer 1

Since,${(7-4\sqrt{2})}^2$

$=49-32-56\sqrt{2}$

$=17-56\sqrt{2}$

$\sqrt{2}$ is irrational ,so is $17-56\sqrt{2}$ and so is .$(7-4\sqrt{2})$