Question

Classify the following number as rational or irrational:
$(\sqrt{2}-2{)}^2$.

Answer 1

Given, $(\sqrt{2}-2{)}^2$.

$(\sqrt{2}-2{)}^2$

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

=$2-4\sqrt{2}+4$

=$6-4\sqrt{2}$.

Here $6$ is a rational number and $4\sqrt{2}$ is an irrational number .

We know, the difference of a rational and an irrational number is an irrational number .

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