Question

State True or False:

$4-5\sqrt{2}$ is irrational if $\sqrt{2}$ is irrational.

• A. True
• B. False

Answer 1

The correct option is A True

The given number is $4-5\sqrt{2}$

If $\sqrt{2}$ is irrational then $5\sqrt{2}$ is also irrational because product of a rational and a irrational number is also irrational.

Again, we know, the difference of a rational and a irrational number is also irrational.

So, $4-5\sqrt{2}$ is irrational.

Hence, the given statement is $True$.