State, whether the following numbers are rational or irrational.
$(2 + \sqrt{2}) (2 - \sqrt{2}$ )

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Solution

Step: Check whether the expression is rational or irrational.
$(2 + \sqrt{2}) (2 - \sqrt{2})$
$= 2^{2} - (\sqrt{2})^{2}$
$= 4 - 2$
$= 2$
Which is a rational number
Therefore $(2 + \sqrt{2}) (2 - \sqrt{2}$ ) is a rational number

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