Question
Examine, whether the following numbers are rational or irrational: $\big(\sqrt{2}-2\big)^2$

Answer

$\big(\sqrt{2}-2\big)^2$ We have, $\big(\sqrt{2}-2\big)^2$ $=2+4-4\sqrt{2}$ $=6+4\sqrt{2} 6$ is a rational number but $4\sqrt{2}$ is an irrational number. The sum of a rational number and an irrational number is an irrational number, so $\big(\sqrt{2}+\sqrt{4}\big)^2$ is an irrational number.

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