Question

State True or False:

${(\sqrt{2}-2)}^2$ is an irrational number.

• A. True
• B. False

Answer 1

The correct option is A True

${(\sqrt{2}-2)}^2=2+4-4\sqrt{2}=6-4\sqrt{2}$

$\sqrt{2}=\mathrm{1.41421356237...}$

$\sqrt{2}$ is an irrational number, since its decimal representation is non-terminating and repeating.

Hence, $(\sqrt{2}-2{)}^2$ is an irrational number.

Therefore, the given statement is true.